Step by step
The question
Question: describe the move that takes A(2, 1) and B(4, 3) to A'(2, −1) and B'(4, −3).
A(2, 1) and B(4, 3)
A'(2, −1) and B'(4, −3)
1 Draw both shapes
Put the shape on the grid
and its image.
2 Compare A and A'
Look at what happened to the numbers of A: A(2, 1) went to A'(2, −1).
A(2, 1) → A'(2, −1)
x stayed the same.
x stays 2
y changed sign.
y: 1 → −1 sign changes
3 Name the move
So the rule is: (x, y) goes to (x, −y).
(x, y) → (x, −y)
Careful!
Only one sign changed.
That is a flip in an axis.
A half turn changes both signs.
Careful: not rotation 180° ✗
That is the rule of a flip in the x-axis.
So the move is a reflection: in the x-axis.
reflection = in the x-axis
4 Check
Let's check the rule on the other points.
B goes to (4, −3).
That is B'.
B(4, 3) → (4, −3) = B'
Let's look back.
First: draw both shapes.
Then: compare A and A'.
Then: name the move.
Last: check.
Answer
reflection = in the x-axis