Step by step
The question
Question: describe the move that takes A(1, 2), B(3, 2) and C(3, 5) to A'(1, −2), B'(3, −2) and C'(3, −5).
A(1, 2), B(3, 2) and C(3, 5)
A'(1, −2), B'(3, −2) and C'(3, −5)
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(1, 2) went to A'(1, −2).
A(1, 2) → A'(1, −2)
x stayed the same.
x stays 1
y changed sign.
y: 2 → −2 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 (3, −2).
That is B'.
B(3, 2) → (3, −2) = B'
C goes to (3, −5): C'.
Right!
C(3, 5) → (3, −5) = C'
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