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# The Coordinate Plane

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 Sub Topics A coordinate plane is the rectangular plane formed with two number lines: one is vertical number line and the other one is the horizontal number line. In the horizontal number line, at left side, negative numbers are placed and at the right hand side, the positive numbers are placed. In case of vertical axis, upper part contains positive numbers and lower part contains negative numbers. The horizontal line represents the x-axis and the vertical line represents the y-axis. There are four quadrants and two axis in a Coordinate Plane. The x-axis is also named as Abscissa and the other name of y-coordinate is Ordinate. Suppose we have to locate a point, then we require a coordinate which is known as ordered pair and these are Set of ‘x’ values and ‘y’ values. The first coordinate in the ordered pair known as Domain which is usually the x-coordinate, and the second coordinate which is usually the y-coordinate is known as Range. The coordinate plane is a two-dimensional surface on which lines, points and curves are plotted with the help of ordered pair. Origin is the point where 0 is placed and 0 is equidistant from both horizontal and vertical axis. Two axes divide the plane into four quadrants. As we know that coordinate plane is made with the help of convection, convection are also helpful in defining the quadrants, the first quadrant is at the top right side of the plane and rest are counted in anti-clockwise format.

## History of Coordinate Plane

Coordinate plane is a plane which has two axes and four quadrants. Horizontal number lines are along x - axis and vertical number lines are along y - axis. In Coordinate Plane, center Point is known as origin. Its coordinate value is (0, 0). Now, let's have a look on History of Coordinate Plane. Concept of Coordinate plane was given by French mathematician, philosopher and scientist â€œRene Descartesâ€. He was a very strong thinker. Rene Descartes gave the concept of analytic Geometry and Cartesian coordinates and Cartesian curve. Coordinate plane was first invented in 1637 by Descartes and Pierre de Fermat. Fermat also worked on three dimensions, but he did not publish his discovery. Both authors used single axis. Invention of coordinate plane system plays an important role in development of Calculus, that was given by Isaac Newton and Gottfried Wilhelm Leibniz. Since times of Descartes, many different coordinate system has been invented, such as, polar coordinate, that was given for plane, spherical and cylindrical coordinate, that was given for three dimensional space.

Figure of coordinate plane is shown below:

In the above figure, we can see that there are four quadrants and two axes. x - axis is plotted along horizontal line and y - axis is plotted along vertical line. As we know that in first quadrant, value of all Trigonometric Functions is positive. In case of second quadrant, only sin function is positive, rest all are negative. In third quadrant, tan function is positive and rest of the values is negative. In last or fourth quadrant, cos is positive and the rest are negative. In coordinate plane, positive values are plotted along right and upper side of origin and negative values are plotted along left side and lower side of origin point. This is all about the history of coordinate plane.

## Coordinate Plane Definition

Coordinate plane is a two-dimensional plane surface on which points are plotted and located in x an y coordinates. It is a two dimensional plane surface, on which we cannot only plot points, but also lines and curves. There are two scales, x axis and y axis at the right angles. Two numbers - the x and y are used to locate the points on the plane, forming the horizontal and the vertical distances of the point from a particular location called the origin.

## Graphing Coordinate Plane

Given below are some solved examples which will give you the right idea on how to graph coordinate plane.

### Solved Examples

Question 1: For a given equation, plot x and y coordinate plane, y = 3x + 7
Solution:
First, let us calculate the x and y values.
So, let us find out the ordered pairs
So, substitute x = 1, 2, 3, 4, 5

When x = 1, we get
y = 3 + 7
y = 10

When x = 2
y = 3 (2) + 7
y = 13

When x = 3
y = 3(3) + 7
y = 16

When x = 4
y = 3(4) + 7
y = 19

When x = 5
y = 3(5) + 7
y = 22

The order pairs of the given equation are
(1, 10), (2, 13), (3, 16), (4, 19), (5, 22)

Question 2: Plot a graph for the given equation y = 2x + 1
Solution:
Given: y = 2x + 1

First, let us calculate the x and y values. So, let us find out the ordered pairs.
So, substitute x = 1, 2, 3, 4, 5
When x = 1, we get
y = 2 + 1
y = 3

When x  = 2
y = 2 (2) + 1
y = 5

When x = 3
y = 2 (3) + 1
y = 7

When x = 4
y = 2 (4) + 1
y = 9

When x = 5
y = 2 (5) + 1
y = 11

The order pairs of the given equation are
(1, 3), (2, 5), (3, 7), (4, 9), (5, 11)

Question 3: Plot a graph for the given equation y = 4x - 1
Solution:
Given: y= 4x - 1

First, let us calculate the x and y values. So, let us find out the ordered pairs
So, substitute x = 1, 2, 3, 4, 5
When x = 1, we get
y = 4 - 1
y = 3

When x = 2
y = 4 (2) - 1
y = 7

When x = 3
y = 4 (3) - 1
y = 11

When x = 4
y = 4 (4) - 1
y = 15

When x = 5
y = 4 (5) - 1
y = 19

The order pairs of the given equation are
(1, 3), (2, 7), (3, 11), (4, 15), (5, 19)