Step by step
The question
Question: describe the move that takes A(2, 1), B(4, 1) and C(2, 3) to A'(−1, 2), B'(−1, 4) and C'(−3, 2).
A(2, 1), B(4, 1) and C(2, 3)
A'(−1, 2), B'(−1, 4) and C'(−3, 2)
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'(−1, 2).
A(2, 1) → A'(−1, 2)
The two numbers swapped places.
2 and 1 swap places
And the new first number got a minus sign.
the new x gets a minus
3 Name the move
So the rule is: (x, y) goes to (−y, x).
(x, y) → (−y, x)
Careful!
A swap alone would be a flip in the line y = x.
Here one number also changed sign.
That is a turn.
Careful: not reflection in y = x ✗
That is the rule of a turn about O.
So the move is a rotation of 90° counterclockwise about the origin.
rotation = 90° counterclockwise
4 Check
Let's check the rule on the other points.
B goes to (−1, 4).
That is B'.
B(4, 1) → (−1, 4) = B'
C goes to (−3, 2): C'.
Right!
C(2, 3) → (−3, 2) = C'
Let's look back.
First: draw both shapes.
Then: compare A and A'.
Then: name the move.
Last: check.
Answer
rotation = 90° counterclockwise