Step by step
The question
Question: dilate the shape A(1, 1), B(3, 1), C(3, 2) and D(1, 2) by scale factor 2.
1 Draw the shape
Put the points on the grid and join them.
2 Multiply each point
Scale factor 2 makes the shape 2 times as big.
Every number is multiplied by 2.
We call the new point A prime.
The little mark means: the new A.
A is (1, 1).
2 times 1 is 2.
2 times 1 is 2.
So A' is (2, 2).
Careful!
A dilation multiplies.
Adding 2 would slide the shape, not make it bigger.
B: 2 times 3 is 6, 2 times 1 is 2.
So B' is (6, 2).
C: 2 times 3 is 6, 2 times 2 is 4.
So C' is (6, 4).
D: 2 times 1 is 2, 2 times 2 is 4.
So D' is (2, 4).
3 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(2, 2), B'(6, 2), C'(6, 4) and D'(2, 4).
4 What changes
Count the flat side AB on the grid: 2 squares.
A'B' is 4 squares.
That is 2 times as long.
Every length is multiplied by 2.
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 2, up 2.
That is 2 times the moves to A.
So A' is on the same line from O, 2 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.