Step by step
The question
Question: describe the move that takes A(1, 3), B(2, 5) and C(4, 3) to A'(3, 1), B'(5, 2) and C'(3, 4).
A(1, 3), B(2, 5) and C(4, 3)
A'(3, 1), B'(5, 2) 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(1, 3) went to A'(3, 1).
A(1, 3) → A'(3, 1)
The two numbers swapped places.
1 and 3 swap places
No sign changed.
no sign changes
3 Name the move
So the rule is: (x, y) goes to (y, x).
(x, y) → (y, x)
Careful!
Swapping alone is a flip in the line y = x.
A quarter turn also changes one sign.
Careful: not rotation 90° ✗
That is the rule of a flip in the line y = x.
So the move is a reflection: in the line y = x.
reflection = in the line y = x
4 Check
Let's check the rule on the other points.
B goes to (5, 2).
That is B'.
B(2, 5) → (5, 2) = 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
reflection = in the line y = x