Everything Maths Grade 10

8 Analytical geometry

Analytical geometry is the study of geometric properties, relationships and measurement of points, lines and
angles in the Cartesian plane. Geometrical shapes are defined using a coordinate system and algebraic princi-
ples. Some consider the introduction of analytical geometry, also called coordinate or Cartesian geometry, to
be the beginning of modern mathematics.

Figure 8.1:The motion of a projectile can be plotted on the Cartesian plane. Animators use this information to help them
create animations.

8.1 Drawing figures on the Cartesian plane EMA68

If we are given the coordinates of the vertices of a figure, we can draw the figure on the Cartesian plane. For
example, quadrilateralABCDwith coordinatesA(1; 1),B(3; 1),C(3; 3)andD(1; 3).

NOTE:

You might also see coordinates written asA(1;1).

1 2 3 4

1

2

3

4

B

D C

A

x

y

The order of the letters for naming a figure is important. It indicates the order in which points must be joined:
AtoB,BtoC,CtoDandDback toA. So the above quadrilateral can be referred to as quadrilateralABCD
orCBADorBADC. However it is conventional to write the letters in alphabetical order and so we only refer
to the quadrilateral asABCD.

VISIT:

You can use an online tool to help you when plotting points on the Cartesian plane. Click here to try this one

onmathsisfun.com.

284 8.1. Drawing figures on the Cartesian plane