Maths revision course by Miriam Hanks

1

Coordinate Geometry

Coordinate geometry is the study of shapes and lines.

When is it used in real life?

Maths revision course by Miriam Hanks

2

Coordinate Geometry in real life

Architects use it to construct

buildings, bridges and roads

Car designers use CAD

Astrophysicists use it to find

the distances between planets

Medical imaging techniques

such as a CAT scanners use it

Maths revision course by Miriam Hanks

3

Gradients

The gradient m is the slope.

For straight lines, use:

or12

12

xx

yym

m =tan θ

m = 1

m = 2

m = 0

Maths revision course by Miriam Hanks

4

Parallel and perpendicular

same gradient

Gradients flip and change sign

Parallel lines:

Perpendicular lines:

2

3

3

2andeg

Maths revision course by Miriam Hanks

5

Equations of straight lines

The equation of a straight line is:

or y = mx + c y – b = m(x – a)

Maths revision course by Miriam Hanks

6

Midpoint formula

find the mean of the twox-coordinates,

and then the mean of the two y-coordinates

Midpoint

Midpoint

To find the midpoint:

Maths revision course by Miriam Hanks

7

Distance formula

The distance formula uses Pythagoras with the CHANGE in the horizontal and vertical distances.

(x2, y2)

(x1, y1)

x2 – x1

y2 – y1

212

212 )()( yyxxDist

Maths revision course by Miriam Hanks

8

Medians

A median of a triangle goes from one point to the midpoint of the line opposite:

Maths revision course by Miriam Hanks

9

Altitudes

An altitude of a triangle goes from one point straight down to meet the opposite side at a right-angle:

Maths revision course by Miriam Hanks

10

Perpendicular bisectors

A perpendicular bisector cuts a line at its midpoint AND at right-angles

and so would not necessarily go through the corner of the triangle.