Step by step
The question
Question: rotate the shape A(2, 1), B(4, 1) and C(4, 2) 180°, then translate it right 3, up 1.
1 Draw the shape
Put the points on the grid and join them.
2 First: rotate 180°
Rotation 180°: both numbers stay in their places, and both change sign.
The rule is: (x, y) goes to (−x, −y).
A(2, 1) goes to A'(−2, −1).
B(4, 1) goes to B'(−4, −1).
C(4, 2) goes to C'(−4, −2).
Join them.
This is the first image.
3 Then: translate
Translation right 3, up 1: right 3 adds 3 to x, up 1 adds 1 to y.
The rule is: (x, y) goes to (x + 3, y + 1).
A'(−2, −1) goes to A''(1, 0).
Careful!
The second move starts from the new points A', B' and C'.
Not from the first shape.
B'(−4, −1) goes to B''(−1, 0).
C'(−4, −2) goes to C''(−1, −1).
Join them.
This is the final image.
So the final image is A''(1, 0), B''(−1, 0) and C''(−1, −1).
4 Check
Let's check in one go.
Put the first rule's answer (−x, −y) into the second rule.
We get (−x + 3, −y + 1).
A goes straight to (1, 0).
That is A''.
Right!
Let's look back.
First: draw the shape.
Then: rotate 180°.
Then: translate right 3, up 1.
Last: check.