A rectangular coordinate system is a pair of perpendicular coordinate lines, called coordinate axes, that are placed so that they intersect at their origin.
The designation of the coordinate axes with the letters x and y is generally accepted, but the letters can be any. If the letters x and y are used, then the plane is called xy-plane. Different applications may use letters other than x and y, and as shown in the figures below, there are uv planes and ts-plane.
Ordered Pair
By an ordered pair of real numbers, we mean two real numbers in a particular order. Each point P in coordinate plane can be related to a unique ordered pair of real numbers by drawing two lines through the point P, one perpendicular to the x-axis and the other perpendicular to the y-axis.
For example, if we take (a,b)=(4,3), then on the coordinate strip
To build a point P(a,b) means to define a point with coordinates (a,b) on the coordinate plane. For example, various points built in the figure below.
In a rectangular coordinate system, the coordinate axes divide the plane into four regions called quadrants. They are numbered counterclockwise with Roman numerals, as shown in the figure.
Graph definition
schedule equation with two variables x and y, is called the set of points on the xy-plane, the coordinates of which are members of the set of solutions of this equation
Example: draw a graph y = x 2
Because 1/x is undefined when x=0, we can only plot points for which x ≠ 0
Example: Find all intersections with axes
(a) 3x + 2y = 6
(b) x = y 2 -2y
(c) y = 1/x
Let y = 0, then 3x = 6 or x = 2
is the required point of intersection of the x-axis.
Having established that x=0, we find that the point of intersection of the y-axis is the point y=3.
In this way you can solve equation (b), and the solutions for (c) are given below
x-crossing
Let y = 0
1/x = 0 => x cannot be determined, i.e. there is no intersection with the y-axis
Let x = 0
y = 1/0 => y is also undefined, => no intersection with the y-axis
In the figure below, the points (x,y), (-x,y),(x,-y), and (-x,-y) represent the corners of the rectangle.
A graph is symmetrical about the x-axis if for each point (x,y) of the graph, the point (x,-y) is also a point on the graph.
A graph is symmetrical about the y-axis if for each graph point (x,y) the point (-x,y) also belongs to the graph.
A graph is symmetrical about the center of coordinates if for each point (x,y) of the graph, the point (-x,-y) also belongs to this graph.
Definition:
Schedule functions on the coordinate plane is defined as the graph of the equation y = f(x)
Plot f(x) = x + 2
Example 2. Plot f(x) = |x|
Graph coincides with the line y = x for x > 0 and with line y = -x
for x< 0 .
graph of f(x) = -x
Combining these two graphs, we get
graph f(x) = |x|
Example 3 Plot
t(x) \u003d (x 2 - 4) / (x - 2) \u003d
= ((x - 2)(x + 2)/(x - 2)) =
= (x + 2) x ≠ 2
Therefore, this function can be written as
y = x + 2 x ≠ 2
Graph h(x)= x 2 - 4 Or x - 2
plot y = x + 2 x ≠ 2
Example 4 Plot
Graphs of functions with displacement
Assume that the graph of the function f(x) is known
Then we can find graphs
y = f(x) + c - graph of the function f(x), moved
UP by c values
y = f(x) - c - graph of the function f(x), moved
DOWN by c values
y = f(x + c) - graph of the function f(x), moved
LEFT by c values
y = f(x - c) - graph of the function f(x), moved
Right by c values
Example 5. Build
graph y = f(x) = |x - 3| + 2
Move the graph y = |x| 3 values to the RIGHT to get the graph
Move the graph y = |x - 3| UP 2 values to plot y = |x - 3| + 2
Plot
y = x 2 - 4x + 5
Let's transform given equation as follows, adding 4 to both parts:
y + 4 = (x 2 - 4x + 5) + 4 y = (x 2 - 4x + 4) + 5 - 4
y = (x - 2) 2 + 1
Here we see that this graph can be obtained by moving the graph y = x 2 to the right 2 values because x is 2 and up 1 value because +1.
y = x 2 - 4x + 5
Reflections
(-x, y) is the reflection of (x, y) about the y-axis
(x, -y) is the reflection of (x, y) about the x-axis
Plots y = f(x) and y = f(-x) are reflections of each other about the y-axis
Plots y = f(x) and y = -f(x) are reflections of each other about the x-axis
The graph can be obtained by reflection and translation:
draw a graph
Let's find its reflection relative to the y-axis, and get a graph
Move this graph right by 2 values and get a graph
Here is the desired graph
If f(x) is multiplied by a positive constant c, then
graph f(x) shrinks vertically if 0< c < 1
graph f(x) stretches vertically if c > 1
The curve is not a graph y = f(x) for any function f
Mathematics is a rather complex science. Studying it, one has not only to solve examples and problems, but also to work with various figures, and even planes. One of the most used in mathematics is the coordinate system on the plane. Children have been taught how to work with it correctly for more than one year. Therefore, it is important to know what it is and how to work with it correctly.
Let's figure out what this system is, what actions you can perform with it, and also find out its main characteristics and features.
Concept definition
A coordinate plane is a plane on which a particular coordinate system is defined. Such a plane is defined by two straight lines intersecting at a right angle. The point of intersection of these lines is the origin of coordinates. Each point on the coordinate plane is given by a pair of numbers, which are called coordinates.
In the school mathematics course, students have to work quite closely with the coordinate system - build figures and points on it, determine which plane this or that coordinate belongs to, and also determine the coordinates of the point and write or name them. Therefore, let's talk in more detail about all the features of the coordinates. But first, let's touch on the history of creation, and then we'll talk about how to work on the coordinate plane.
History reference
Ideas about creating a coordinate system were in the days of Ptolemy. Even then, astronomers and mathematicians were thinking about how to learn how to set the position of a point on a plane. Unfortunately, at that time there was no coordinate system known to us, and scientists had to use other systems.
Initially, they set points by specifying latitude and longitude. For a long time it was one of the most used ways of mapping this or that information. But in 1637, Rene Descartes created his own coordinate system, later named after "Cartesian".
Already in late XVII in. the concept of "coordinate plane" has become widely used in the world of mathematics. Despite the fact that several centuries have passed since the creation of this system, it is still widely used in mathematics and even in life.
Coordinate plane examples
Before talking about the theory, we will give some illustrative examples of the coordinate plane so that you can imagine it. The coordinate system is primarily used in chess. On the board, each square has its own coordinates - one letter coordinate, the second - digital. With its help, you can determine the position of a particular piece on the board.
The second most striking example is the beloved game "Battleship". Remember how, when playing, you name a coordinate, for example, B3, thus indicating exactly where you are aiming. At the same time, when placing the ships, you set points on the coordinate plane.
This coordinate system is widely used not only in mathematics, logic games, but also in military affairs, astronomy, physics and many other sciences.
Coordinate axes
As already mentioned, two axes are distinguished in the coordinate system. Let's talk a little about them, as they are of considerable importance.
The first axis - abscissa - is horizontal. It is denoted as ( Ox). The second axis is the ordinate, which passes vertically through the reference point and is denoted as ( Oy). It is these two axes that form the coordinate system, dividing the plane into four quarters. The origin is located at the intersection point of these two axes and takes on the value 0 . Only if the plane is formed by two axes intersecting perpendicularly, having a reference point, is it a coordinate plane.
Also note that each of the axes has its own direction. Usually, when constructing a coordinate system, it is customary to indicate the direction of the axis in the form of an arrow. In addition, when constructing the coordinate plane, each of the axes is signed.
quarters
Now let's say a few words about such a concept as quarters of the coordinate plane. The plane is divided by two axes into four quarters. Each of them has its own number, while the numbering of the planes is counterclockwise.
Each of the quarters has its own characteristics. So, in the first quarter, the abscissa and the ordinate are positive, in the second quarter, the abscissa is negative, the ordinate is positive, in the third, both the abscissa and the ordinate are negative, in the fourth, the abscissa is positive, and the ordinate is negative.
By remembering these features, you can easily determine which quarter a particular point belongs to. In addition, this information may be useful to you if you have to do calculations using the Cartesian system.
Working with the coordinate plane
When we figured out the concept of a plane and talked about its quarters, we can move on to such a problem as working with this system, and also talk about how to put points, coordinates of figures on it. On the coordinate plane, this is not as difficult as it might seem at first glance.
First of all, the system itself is built, all important designations are applied to it. Then there is work directly with points or figures. In this case, even when constructing figures, points are first applied to the plane, and then the figures are already drawn.
Rules for constructing a plane
If you decide to start marking shapes and points on paper, you will need a coordinate plane. The coordinates of the points are plotted on it. In order to build a coordinate plane, you only need a ruler and a pen or pencil. First, the horizontal abscissa is drawn, then the vertical - ordinate. It is important to remember that the axes intersect at right angles.
The next obligatory item is marking. Units-segments are marked and signed on each of the axes in both directions. This is done so that you can then work with the plane with maximum convenience.
Marking a point
Now let's talk about how to plot the coordinates of points on the coordinate plane. This is the basics you need to know to successfully place a variety of shapes on the plane, and even mark equations.
When constructing points, one should remember how their coordinates are correctly recorded. So, usually setting a point, two numbers are written in brackets. The first digit indicates the coordinate of the point along the abscissa axis, the second - along the ordinate axis.
The point should be built in this way. Mark on axis first Ox given point, then mark a point on the axis Oy. Next, draw imaginary lines from these designations and find the place of their intersection - this will be the given point.
All you have to do is mark it and sign it. As you can see, everything is quite simple and does not require special skills.
Placing a Shape
Now let's move on to such a question as the construction of figures on the coordinate plane. In order to build any figure on the coordinate plane, you should know how to place points on it. If you know how to do this, then placing a figure on a plane is not so difficult.
First of all, you will need the coordinates of the points of the figure. It is on them that we will apply the ones you have chosen to our coordinate system. Let's consider drawing a rectangle, triangle and circle.
Let's start with a rectangle. Applying it is pretty easy. First, four points are applied to the plane, indicating the corners of the rectangle. Then all points are sequentially connected to each other.
Drawing a triangle is no different. The only thing is that it has three corners, which means that three points are applied to the plane, denoting its vertices.
Regarding the circle, here you should know the coordinates of two points. The first point is the center of the circle, the second is the point denoting its radius. These two points are plotted on a plane. Then a compass is taken, the distance between two points is measured. The point of the compass is placed at a point denoting the center, and a circle is described.
As you can see, there is also nothing complicated here, the main thing is that there is always a ruler and a compass at hand.
Now you know how to plot shape coordinates. On the coordinate plane, this is not so difficult to do, as it might seem at first glance.
conclusions
So, we have considered with you one of the most interesting and basic concepts for mathematics that every student has to deal with.
We have found out that the coordinate plane is the plane formed by the intersection of two axes. With its help, you can set the coordinates of points, put shapes on it. The plane is divided into quarters, each of which has its own characteristics.
The main skill that should be developed when working with the coordinate plane is the ability to correctly apply given points. To do this, you should know the correct location of the axes, the features of the quarters, as well as the rules by which the coordinates of the points are set.
We hope that the information presented by us was accessible and understandable, and was also useful for you and helped to better understand this topic.
The points are “registered” - “residents”, each point has its own “house number” - its coordinate. If the point is taken in a plane, then for its “registration” it is necessary to indicate not only the “house number”, but also the “apartment number”. Recall how this is done.
Let us draw two mutually perpendicular coordinate lines and consider the point of their intersection, the point O, as the starting point on both lines. Thus, a rectangular coordinate system is set on the plane (Fig. 20), which transforms the usual plane to coordinate. The point O is called the origin of coordinates, the coordinate lines (x-axis and y-axis) are called coordinate axes, and the right angles formed by the coordinate axes are called coordinate angles. Coordinate rectangular corners numbered as shown in Figure 20.
And now let's turn to Figure 21, which shows a rectangular coordinate system and marked point M. Let's draw a line through it parallel to the y axis. The line intersects the x-axis at some point, this point has a coordinate - on the x-axis. For the point shown in Figure 21, this coordinate is -1.5, it is called the abscissa of the point M. Next, we draw a straight line through the point M parallel to the x axis. The line intersects the y-axis at some point, this point has a coordinate - on the y-axis.
For point M, shown in Figure 21, this coordinate is 2, it is called the ordinate of the point M. Briefly written like this: M (-1.5; 2). The abscissa is written in the first place, the ordinate - in the second. They use, if necessary, another form of notation: x = -1.5; y = 2.
Remark 1 . In practice, to find the coordinates of the point M, usually instead of straight lines parallel to the coordinate axes and passing through the point M, segments of these straight lines from the point M to the coordinate axes are built (Fig. 22).
Remark 2. In the previous section, we introduced different notation for number gaps. In particular, as we agreed, the notation (3, 5) means that an interval with ends at points 3 and 5 is considered on the coordinate line. In this section, we consider a pair of numbers as coordinates of a point; for example, (3; 5) is a point on coordinate plane with the abscissa 3 and the ordinate 5. How is it correct to determine from the symbolic notation what is at stake: about the interval or about the coordinates of the point? Most of the time this is clear from the text. What if it's not clear? Pay attention to one detail: we used a comma in the interval designation, and a semicolon in the coordinate designation. This, of course, is not very significant, but still the difference; we will apply it.
Given the terms and notation introduced, the horizontal coordinate line is called the abscissa, or x-axis, and the vertical coordinate line is called the y-axis, or y-axis. The designations x, y are usually used when specifying a rectangular coordinate system on the plane (see Fig. 20) and they often say this: the xOy coordinate system is given. However, there are other designations: for example, in Figure 23, the coordinate system tOs is given.
Algorithm for finding the coordinates of the point M, given in the rectangular coordinate system хОу
This is exactly how we acted, finding the coordinates of the point M in Figure 21. If the point M 1 (x; y) belongs to the first coordinate angle, then x\u003e 0, y\u003e 0; if the point M 2 (x; y) belongs to the second coordinate angle, then x< 0, у >0; if the point M 3 (x; y) belongs to the third coordinate angle, then x< О, у < 0; если точка М 4 (х; у) принадлежит четвертому координатному углу, то х >OU< 0 (рис. 24).
But what happens if the point whose coordinates need to be found lies on one of the coordinate axes? Let point A lie on the x-axis, and point B lie on the y-axis (Fig. 25). It makes no sense to draw a straight line parallel to the y-axis through point A and find the point of intersection of this line with the x-axis, since there is already such an intersection point - this is point A, its coordinate (abscissa) is 3. In the same way, you do not need to draw through the point And the line parallel to the x-axis - this line is the x-axis itself, which intersects the y-axis at point O with coordinate (ordinate) 0. As a result, for point A we get A (3; 0). Similarly, for point B we get B(0; - 1.5). And for the point O we have O(0; 0).
In general, any point on the x-axis has coordinates (x; 0), and any point on the y-axis has coordinates (0; y)
So, we discussed how to find the coordinates of a point in the coordinate plane. But how to solve the inverse problem, i.e., how, having given the coordinates, to construct the corresponding point? To develop an algorithm, we will carry out two auxiliary, but at the same time important arguments.
First discussion. Let I be drawn in the xOy coordinate system, parallel to the y axis and intersecting the x axis at a point with coordinate (abscissa) 4
(Fig. 26). Any point lying on this line has an abscissa 4. So, for points M 1, M 2, M 3 we have M 1 (4; 3), M 2 (4; 6), M 3 (4; - 2). In other words, the abscissa of any point M of the straight line satisfies the condition x \u003d 4. They say that x \u003d 4 - the equation line l or that line I satisfies the equation x = 4.
Figure 27 shows lines that satisfy the equations x = - 4 (line I 1), x = - 1
(straight line I 2) x = 3.5 (straight line I 3). And which line satisfies the equation x = 0? Guessed? y axis
Second discussion. Let a straight line I be drawn in the xOy coordinate system, parallel to the x-axis and intersecting the y-axis at a point with coordinate (ordinate) 3 (Fig. 28). Any point lying on this line has an ordinate of 3. So, for points M 1, M 2, M 3 we have: M 1 (0; 3), M 2 (4; 3), M 3 (- 2; 3) . In other words, the ordinate of any point M of the line I satisfies the condition y \u003d 3. They say that y \u003d 3 is the equation of line I or that line I satisfies the equation y \u003d 3.
Figure 29 shows lines that satisfy the equations y \u003d - 4 (line l 1), y \u003d - 1 (line I 2), y \u003d 3.5 (line I 3) - A which line satisfies the equation y \u003d 01 Guess? x axis.
Note that mathematicians, striving for brevity of speech, say "a straight line x = 4", and not "a straight line that satisfies the equation x = 4". Likewise, they say "line y = 3", not "line satisfying y = 3". We will do exactly the same. Let us now return to Figure 21. Please note that the point M (- 1.5; 2), which is shown there, is the intersection point of the line x = -1.5 and the line y = 2. Now, apparently, the algorithm for constructing the point will be clear according to its given coordinates.
Algorithm for constructing a point M (a; b) in a rectangular coordinate system хОу
EXAMPLE In the xOy coordinate system, construct points: A (1; 3), B (- 2; 1), C (4; 0), D (0; - 3).
Solution. Point A is the point of intersection of the lines x = 1 and y = 3 (see Fig. 30).
Point B is the point of intersection of the lines x = - 2 and y = 1 (Fig. 30). Point C belongs to the x-axis, and point D belongs to the y-axis (see Fig. 30).
In conclusion of the section, we note that for the first time a rectangular coordinate system on the plane began to be actively used to replace algebraic models geometric French philosopher René Descartes (1596-1650). Therefore, sometimes they say "Cartesian coordinate system", "Cartesian coordinates".
A complete list of topics by class, calendar plan according to school curriculum math online, footage in mathematics for grade 7 download
A. V. Pogorelov, Geometry for grades 7-11, Textbook for educational institutions
Lesson content lesson summary support frame lesson presentation accelerative methods interactive technologies Practice tasks and exercises self-examination workshops, trainings, cases, quests homework discussion questions rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures graphics, tables, schemes humor, anecdotes, jokes, comics parables, sayings, crossword puzzles, quotes Add-ons abstracts articles chips for inquisitive cheat sheets textbooks basic and additional glossary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in the textbook elements of innovation in the lesson replacing obsolete knowledge with new ones Only for teachers perfect lessons calendar plan for the year guidelines discussion programs Integrated LessonsA rectangular coordinate system on a plane is formed by two mutually perpendicular coordinate axes X'X and Y'Y. The coordinate axes intersect at point O, which is called the origin of coordinates, a positive direction is chosen on each axis. The positive direction of the axes (in the right-handed coordinate system) is chosen so that when the X'X axis is rotated counterclockwise by 90 °, its positive direction coincides with the positive direction of the Y'Y axis. The four angles (I, II, III, IV) formed by the X'X and Y'Y coordinate axes are called coordinate angles (see Fig. 1).
The position of point A on the plane is determined by two coordinates x and y. The x-coordinate is equal to the length of the OB segment, the y-coordinate is the length of the OC segment in the selected units. Segments OB and OC are defined by lines drawn from point A parallel to the Y’Y and X’X axes, respectively. The x coordinate is called the abscissa of point A, the y coordinate is called the ordinate of point A. They write it like this: A (x, y).
If point A lies in coordinate angle I, then point A has positive abscissa and ordinate. If point A lies in coordinate angle II, then point A has a negative abscissa and a positive ordinate. If point A lies in coordinate angle III, then point A has negative abscissa and ordinate. If point A lies in coordinate angle IV, then point A has a positive abscissa and a negative ordinate.
Rectangular coordinate system in space is formed by three mutually perpendicular coordinate axes OX, OY and OZ. The coordinate axes intersect at the point O, which is called the origin of coordinates, on each axis the positive direction indicated by the arrows is chosen, and the unit of measurement of the segments on the axes. The units of measure are the same for all axes. OX - abscissa axis, OY - ordinate axis, OZ - applicate axis. The positive direction of the axes is chosen so that when the OX axis is rotated counterclockwise by 90°, its positive direction coincides with the positive direction of the OY axis, if this rotation is observed from the positive direction of the OZ axis. Such a coordinate system is called right. If the thumb right hand take for the X direction, the index for the Y direction, and the middle one for the Z direction, then a right-handed coordinate system is formed. Similar fingers of the left hand form the left coordinate system. The right and left coordinate systems cannot be combined so that the corresponding axes coincide (see Fig. 2).
The position of point A in space is determined by three coordinates x, y and z. The x coordinate is equal to the length of the segment OB, the y coordinate is equal to the length of the segment OC, the z coordinate is the length of the segment OD in the selected units. The segments OB, OC and OD are defined by planes drawn from point A parallel to the planes YOZ, XOZ and XOY, respectively. The x coordinate is called the abscissa of point A, the y coordinate is called the ordinate of point A, the z coordinate is called the applicate of point A. They write it like this: A (a, b, c).
Horts
A rectangular coordinate system (of any dimension) is also described by a set of orts , co-directed with the coordinate axes. The number of orts is equal to the dimension of the coordinate system, and they are all perpendicular to each other.
In the three-dimensional case, such vectors are usually denoted i j k or e x e y e z . Meanwhile, in the case right system coordinates, the following formulas with the cross product of vectors are valid:
- [i j]=k ;
- [j k]=i ;
- [k i]=j .
Story
René Descartes was the first to introduce a rectangular coordinate system in his Discourse on the Method in 1637. Therefore, the rectangular coordinate system is also called - Cartesian system coordinates. The coordinate method for describing geometric objects laid the foundation for analytical geometry. Pierre Fermat also contributed to the development of the coordinate method, but his work was first published after his death. Descartes and Fermat used the coordinate method only on the plane.
The coordinate method for three-dimensional space was first applied by Leonhard Euler already in the 18th century.
see also
Links
Wikimedia Foundation. 2010 .
See what the "Coordinate plane" is in other dictionaries:
cutting plane- (Pn) Coordinate plane tangent to the cutting edge at the considered point and perpendicular to the base plane. […
In topography, a network of imaginary lines encircling Earth in the latitudinal and meridional directions, with which you can accurately determine the position of any point on earth's surface. Latitudes are measured from the equator - a great circle, ... ... Geographic Encyclopedia
In topography, a network of imaginary lines encircling the globe in the latitudinal and meridional directions, with which you can accurately determine the position of any point on the earth's surface. Latitudes are measured from the equator of the great circle, ... ... Collier Encyclopedia
This term has other meanings, see Phase diagram. The phase plane is the coordinate plane in which any two variables (phase coordinates) are plotted along the coordinate axes, which uniquely determine the state of the system ... ... Wikipedia
principal cutting plane- (Pτ) Coordinate plane perpendicular to the line of intersection of the main plane and the cutting plane. [GOST 25762 83] Topics of cutting Generalizing terms systems of coordinate planes and coordinate planes … Technical Translator's Handbook
instrumental principal cutting plane- (Pτi) Coordinate plane perpendicular to the line of intersection of the instrumental main plane and the cutting plane. [GOST 25762 83] Topics of cutting Generalizing terms systems of coordinate planes and coordinate planes … Technical Translator's Handbook
tool cutting plane- (Pni) Coordinate plane tangent to the cutting edge at the point in question and perpendicular to the instrument base plane. [GOST 25762 83] Topics for cutting Generalizing terms for systems of coordinate planes and ... ... Technical Translator's Handbook
kinematic principal cutting plane- (Pτк) Coordinate plane perpendicular to the line of intersection of the kinematic main plane and the cutting plane ... Technical Translator's Handbook
kinematic cutting plane- (Pnk) Coordinate plane tangent to the cutting edge at the point under consideration and perpendicular to the kinematic base plane ... Technical Translator's Handbook
main plane- (Pv) A coordinate plane drawn through the considered point of the cutting edge perpendicular to the direction of the velocity of the main or net cutting motion at that point. Note In the instrumental coordinate system, the direction ... ... Technical Translator's Handbook
To indicate the relative position of some objects under study, the following are used:
- coordinate beam, when their placement or movement occurs along a straight line on one side of a given object, taken as the origin;
- coordinate line, when their placement or movement occurs along a straight line on opposite sides of a given object, taken as a reference point;
- coordinate plane when their placement or movement occurs along an arbitrary non-straight line.
Elements of the coordinate plane
A coordinate plane differs from an ordinary plane in that a coordinate system is applied to it. An example is the image of any continent with parallels and meridians plotted on it, which define the system geographical coordinates, allowing you to find or set the position of any object on the map.
The coordinate system consists of two coordinate lines mutually intersecting at right angles at the points of reference. It is customary to call the horizontal coordinate line the abscissa axis (the abscissa in Latin is a segment). The vertical line - the ordinate axis (ordinate from Latin - alignment in order).
Similarly, the coordinate line differs from the usual line in that some point is chosen on it for the origin; choose the scale of a single segment, depending on what distances are to be depicted; the positive reference direction, indicated on the coordinate straight arrow.
The position of an object on such a plane is indicated by a point with two numbers - coordinates: the abscissa and the ordinate.
Using coordinate planes
Coordinate planes are widely used to solve geometric and physical problems. Moreover, in physics, the abscissa is often taken as the time axis. Then the y-axis sets the coordinate of the body on the coordinate line located along the rectilinear trajectory of the body.
