Step by step
The question
Question: describe the move that takes A(1, 2), B(4, 2) and C(1, 3) to A'(5, 2), B'(2, 2) and C'(5, 3).
A(1, 2), B(4, 2) and C(1, 3)
A'(5, 2), B'(2, 2) and C'(5, 3)
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'(5, 2).
A(1, 2) → A'(5, 2)
y stays 2.
y stays 2
x went from 1 to 5.
Halfway between them: add, then divide by 2.
That is 3.
x: 1 → 5, halfway: 1 + 52 = 3
3 Name the move
So the rule is: (x, y) goes to (−x + 6, y).
(x, y) → (−x + 6, y)
Careful!
The other points do not move the same way.
They flip over the line x = 3.
Careful: not a translation ✗
That is the rule of a flip in the line x = 3.
So the move is a reflection: in the line x = 3.
reflection = in the line x = 3
4 Check
Let's check the rule on the other points.
B goes to (2, 2).
That is B'.
B(4, 2) → (2, 2) = B'
C goes to (5, 3): C'.
Right!
C(1, 3) → (5, 3) = 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 x = 3