Step by step
The question
Question: translate the shape A(1, 1), B(3, 1) and C(1, 3) right 2, up 1, then dilate it scale factor 2.
1 Draw the shape
Put the points on the grid and join them.
2 First: translate
Translation right 2, up 1: right 2 adds 2 to x, up 1 adds 1 to y.
The rule is: (x, y) goes to (x + 2, y + 1).
A(1, 1) goes to A'(3, 2).
B(3, 1) goes to B'(5, 2).
C(1, 3) goes to C'(3, 4).
Join them.
This is the first image.
3 Then: dilate by scale factor 2
Dilation scale factor 2: both numbers are multiplied by 2.
The rule is: (x, y) goes to (2x, 2y).
A'(3, 2) goes to A''(6, 4).
Careful!
The second move starts from the new points A', B' and C'.
Not from the first shape.
B'(5, 2) goes to B''(10, 4).
C'(3, 4) goes to C''(6, 8).
Join them.
This is the final image.
So the final image is A''(6, 4), B''(10, 4) and C''(6, 8).
4 Check
Let's check in one go.
Put the first rule's answer (x + 2, y + 1) into the second rule.
We get (2x + 4, 2y + 2).
A goes straight to (6, 4).
That is A''.
Right!
Let's look back.
First: draw the shape.
Then: translate right 2, up 1.
Then: dilate by scale factor 2.
Last: check.