Step by step
The question
Question: dilate the shape A(4, 2), B(8, 2) and C(4, 6) by scale factor ½.
1 Draw the shape
Put the points on the grid and join them.
2 Multiply each point
Scale factor one half makes the shape half as big.
Every number is multiplied by one half.
We call the new point A prime.
The little mark means: the new A.
A is (4, 2).
Half of 4 is 2.
Half of 2 is 1.
So A' is (2, 1).
Careful!
Half as big means divide every number by 2.
Taking 2 away would slide the shape.
B: half of 8 is 4, half of 2 is 1.
So B' is (4, 1).
C: half of 4 is 2, half of 6 is 3.
So C' is (2, 3).
3 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(2, 1), B'(4, 1) and C'(2, 3).
4 What changes
Count the flat side AB on the grid: 4 squares.
A'B' is 2 squares.
That is half as long.
Every length is multiplied by one half.
The angles do not change.
The image is the same shape, just smaller.
5 Check
Let's check A.
Draw a line from O through A' to A.
From O to A: right 4, up 2.
From O to A': right 2, up 1.
That is half the moves to A.
So A' is on the same line from O, half as far.
Right!
Let's look back.
First: draw the shape.
Then: multiply each point.
Then: draw the image.
Then: what changes.
Last: check.