1. Maths revision course by Miriam Hanks
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. Maths revision course by Miriam Hanks
Gradients
The gradient m is the slope.
For straight lines, use: or
m = 2
m = 1
m = 0
m =tan θ
Maths revision course by Miriam Hanks

4. Parallel and perpendicular
Parallel lines:
same gradient
Gradients flip and change sign
Perpendicular lines:
Maths revision course by Miriam Hanks

5. Equations of straight lines
The equation of a straight line is: or
y – b = m(x – a)
y = mx + c
Maths revision course by Miriam Hanks

6. Maths revision course by Miriam Hanks
Midpoint formula
To find the midpoint:
find the mean of the two
x-coordinates,
and then the mean of the two y-coordinates
Midpoint
Midpoint
Maths revision course by Miriam Hanks

7. Maths revision course by Miriam Hanks
Distance formula
The distance formula uses Pythagoras with the CHANGE in the horizontal and vertical distances.
(x2, y2)
y2 – y1
(x1, y1)
x2 – x1
Maths revision course by Miriam Hanks

8. Maths revision course by Miriam Hanks
Medians
A median of a triangle goes from one point to the midpoint of the line opposite:
Maths revision course by Miriam Hanks

9. Maths revision course by Miriam Hanks
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.
Maths revision course by Miriam Hanks