Coordinates (age 12+)
Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids
What a learner can do afterwards
- Enlarge a shape by a given scale factor from a specified centre of enlargement
- Determine the scale factor between two similar shapes by comparing corresponding sides
- Explain why corresponding angles in similar shapes are equal while sides are in proportion
The lesson
Enlargement is a transformation that makes a shape bigger or smaller without changing its shape. You need two things: a centre of enlargement, which is a fixed point, and a scale factor, which tells you how many times bigger or smaller each length becomes.
To enlarge from the origin, multiply every coordinate by the scale factor. Triangle ABC has corners at (1, 1), (3, 1), and (1, 4). Enlarged by scale factor 2 from the origin, the new corners are (2, 2), (6, 2), and (2, 8).
When the centre is not the origin, you cannot just multiply the coordinates. Instead, work out how far each corner is from the centre, multiply that distance by the scale factor, then measure the same distance out from the centre in the same direction.
Corresponding angles never change in an enlargement. Only the side lengths change, and every side scales by the same factor. That constant ratio is what makes the two shapes similar.
Enlargement keeps every angle the same while every length grows or shrinks by one constant scale factor measured from the centre.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.