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GRADE 10 Cartesian Plane

The document explains the concept of the coordinate plane, also known as the Cartesian plane, which consists of two perpendicular axes, x and y. It provides formulas for calculating the gradient, midpoint, and distance between points, as well as instructions on how to plot points using ordered pairs. An exercise is included for practice in plotting specific points on the coordinate plane.

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49 views4 pages

GRADE 10 Cartesian Plane

The document explains the concept of the coordinate plane, also known as the Cartesian plane, which consists of two perpendicular axes, x and y. It provides formulas for calculating the gradient, midpoint, and distance between points, as well as instructions on how to plot points using ordered pairs. An exercise is included for practice in plotting specific points on the coordinate plane.

Uploaded by

angelinanonhlanhla08
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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GRADE 10 - CO-ORDINATE GEOMETRY

What is a Coordinate Plane or Cartesian Plane?


The coordinate plane or Cartesian plane is a basic concept for coordinate geometry.
It describes a two-dimensional plane in terms of two perpendicular axes: x and y.
The x-axis indicates the horizontal direction while the y-axis indicates the vertical
direction of the plane. In the coordinate plane, points are indicated by their
positions along the x and y-axes
Coordinate Geometry Formulas
The following table gives some coordinate geometry formulas.

FORMULA
1. Gradient/Slope y 2− y 1
x 2−x 1

( x +2 x ; y +2 y )
2. Midpoint 1 2 1 2

3. Distance
√(x ¿ ¿ 2−x ) +( y − y ) ¿
1
2
2 1
2
How to plot points in the coordinate plane and how to determine the
coordinates of points on the coordinate plane?
To graph or plot points, we use two perpendicular lines called axes. The point at
which the axes cross is called the origin. Arrows in the axes indicate the positive
directions.
Consider the ordered pair (4, 3). The numbers in an ordered pair are called the
coordinates. The first coordinate or x-coordinate in this case is 4 and the second
coordinate or y-coordinate is 3.
To plot the point (4, 3) we start at the origin, move horizontally to the right 4 units,
move up vertically 3 units, and then make a point.

For example: In the coordinate plane below, point L is represented by the


coordinates (–3, 1.5) because it is positioned on –3 along the x-axis and on 1.5
along the y-axis. Similarly, you can figure out the positions for the points M = (2,
1.5) and N = (–2, –3).

Exercise 1
Use the Cartesian plane above to plot the following points: A(-3,2), B(-1,4), C(-2,-4),
D(0,-2), E(3,0)

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