Step by step
The question
Question: describe the move that takes A(−3, 1), B(−1, 1) and C(−1, 3) to A'(−3, −3), B'(−1, −3) and C'(−1, −5).
A(−3, 1), B(−1, 1) and C(−1, 3)
A'(−3, −3), B'(−1, −3) and C'(−1, −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(−3, 1) went to A'(−3, −3).
A(−3, 1) → A'(−3, −3)
x stays −3.
x stays −3
y went from 1 to −3.
Halfway between them: add, then divide by 2.
That is −1.
y: 1 → −3, halfway: 1 + (−3)2 = −1
3 Name the move
So the rule is: (x, y) goes to (x, −y − 2).
(x, y) → (x, −y − 2)
Careful!
The other points do not move the same way.
They flip over the line y = −1.
Careful: not a translation ✗
That is the rule of a flip in the line y = −1.
So the move is a reflection: in the line y = −1.
reflection = in the line y = −1
4 Check
Let's check the rule on the other points.
B goes to (−1, −3).
That is B'.
B(−1, 1) → (−1, −3) = B'
C goes to (−1, −5): C'.
Right!
C(−1, 3) → (−1, −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 line y = −1