Step by step
The question
Question: dilate the shape A(1, 1), B(2, 1), C(2, 2) and D(1, 2) by scale factor 3.
1 Draw the shape
Put the points on the grid and join them.
2 Multiply each point
Scale factor 3 makes the shape 3 times as big.
Every number is multiplied by 3.
We call the new point A prime.
The little mark means: the new A.
A is (1, 1).
3 times 1 is 3.
3 times 1 is 3.
So A' is (3, 3).
Careful!
A dilation multiplies.
Adding 3 would slide the shape, not make it bigger.
B: 3 times 2 is 6, 3 times 1 is 3.
So B' is (6, 3).
C: 3 times 2 is 6, 3 times 2 is 6.
So C' is (6, 6).
D: 3 times 1 is 3, 3 times 2 is 6.
So D' is (3, 6).
3 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(3, 3), B'(6, 3), C'(6, 6) and D'(3, 6).
4 What changes
Count the flat side AB on the grid: 1 squares.
A'B' is 3 squares.
That is 3 times as long.
Every length is multiplied by 3.
The angles do not change.
The image is the same shape, just bigger.
5 Check
Let's check A.
Draw a line from O through A to A'.
From O to A: right 1, up 1.
From O to A': right 3, up 3.
That is 3 times the moves to A.
So A' is on the same line from O, 3 times as far.
Right!
Let's look back.
First: draw the shape.
Then: multiply each point.
Then: draw the image.
Then: what changes.
Last: check.