Step by step
The question
Question: rotate the shape A(1, 1), B(3, 1) and C(1, 2) 90° counterclockwise, then reflect it in the x-axis.
1 Draw the shape
Put the points on the grid and join them.
2 First: rotate 90° counterclockwise
Rotation 90° counterclockwise: the two numbers swap places, and the new first number gets a minus sign.
The rule is: (x, y) goes to (−y, x).
A(1, 1) goes to A'(−1, 1).
B(3, 1) goes to B'(−1, 3).
C(1, 2) goes to C'(−2, 1).
Join them.
This is the first image.
3 Then: reflect in the x-axis
Reflection in the x-axis: x stays the same, y changes sign.
The rule is: (x, y) goes to (x, −y).
A'(−1, 1) goes to A''(−1, −1).
Careful!
The second move starts from the new points A', B' and C'.
Not from the first shape.
B'(−1, 3) goes to B''(−1, −3).
C'(−2, 1) goes to C''(−2, −1).
Join them.
This is the final image.
So the final image is A''(−1, −1), B''(−1, −3) and C''(−2, −1).
4 Check
Let's check in one go.
Put the first rule's answer (−y, x) into the second rule.
We get (−y, −x).
A goes straight to (−1, −1).
That is A''.
Right!
Let's look back.
First: draw the shape.
Then: rotate 90° counterclockwise.
Then: reflect in the x-axis.
Last: check.