Step by step
The question
Question: dilate the shape A(2, 2), B(4, 2) and C(2, 4) scale factor ½, then translate it left 4.
1 Draw the shape
Put the points on the grid and join them.
2 First: dilate by scale factor ½
Dilation scale factor ½: both numbers are multiplied by one half.
The rule is: (x, y) goes to (½x, ½y).
A(2, 2) goes to A'(1, 1).
B(4, 2) goes to B'(2, 1).
C(2, 4) goes to C'(1, 2).
Join them.
This is the first image.
3 Then: translate
Translation left 4: left 4 takes 4 from x.
The rule is: (x, y) goes to (x − 4, y).
A'(1, 1) goes to A''(−3, 1).
Careful!
The second move starts from the new points A', B' and C'.
Not from the first shape.
B'(2, 1) goes to B''(−2, 1).
C'(1, 2) goes to C''(−3, 2).
Join them.
This is the final image.
So the final image is A''(−3, 1), B''(−2, 1) and C''(−3, 2).
4 Check
Let's check in one go.
Put the first rule's answer (½x, ½y) into the second rule.
We get (½x − 4, ½y).
A goes straight to (−3, 1).
That is A''.
Right!
Let's look back.
First: draw the shape.
Then: dilate by scale factor ½.
Then: translate left 4.
Last: check.