Step by step
The question
Question: reflect the shape A(1, 1), B(3, 1) and C(1, 4) in the y-axis, then translate it down 2.
1 Draw the shape
Put the points on the grid and join them.
2 First: reflect in the y-axis
Reflection in the y-axis: x changes sign, y stays the same.
The rule is: (x, y) goes to (−x, y).
A(1, 1) goes to A'(−1, 1).
B(3, 1) goes to B'(−3, 1).
C(1, 4) goes to C'(−1, 4).
Join them.
This is the first image.
3 Then: translate
Translation down 2: down 2 takes 2 from y.
The rule is: (x, y) goes to (x, y − 2).
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'(−3, 1) goes to B''(−3, −1).
C'(−1, 4) goes to C''(−1, 2).
Join them.
This is the final image.
So the final image is A''(−1, −1), B''(−3, −1) and C''(−1, 2).
4 Check
Let's check in one go.
Put the first rule's answer (−x, y) into the second rule.
We get (−x, y − 2).
A goes straight to (−1, −1).
That is A''.
Right!
Let's look back.
First: draw the shape.
Then: reflect in the y-axis.
Then: translate down 2.
Last: check.