Step by step
The question
Question: describe the move that takes A(2, 1), B(4, 1) and C(4, 3) to A'(1, −2), B'(1, −4) and C'(3, −4).
A(2, 1), B(4, 1) and C(4, 3)
A'(1, −2), B'(1, −4) and C'(3, −4)
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 second number got a minus sign.
the new y 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° clockwise about the origin.
rotation = 90° clockwise
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, −4): C'.
Right!
C(4, 3) → (3, −4) = C'
Let's look back.
First: draw both shapes.
Then: compare A and A'.
Then: name the move.
Last: check.
Answer
rotation = 90° clockwise