Step by step
The question
Question: describe the move that takes A(4, 2), B(8, 2) and C(4, 6) to A'(2, 1), B'(4, 1) and C'(2, 3).
A(4, 2), B(8, 2) and C(4, 6)
A'(2, 1), B'(4, 1) and C'(2, 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(4, 2) went to A'(2, 1).
A(4, 2) → A'(2, 1)
x went from 4 to 2: half of it.
x: 4 → 2 is × ½
y went from 2 to 1: half of it too.
y: 2 → 1 is × ½
3 Name the move
So the rule is: (x, y) goes to (½x, ½y).
(x, y) → (12x, 12y)
Careful!
The moves are not the same for every point.
They grow with the point.
That is multiplying: a dilation.
Careful: not a translation ✗
That is the rule of a dilation: A and A' are on one line from O.
So the move is a dilation with scale factor ½, from the origin.
dilation = scale factor ½
4 Check
Let's check the rule on the other points.
B goes to (4, 1).
That is B'.
B(8, 2) → (4, 1) = B'
C goes to (2, 3): C'.
Right!
C(4, 6) → (2, 3) = C'
Let's look back.
First: draw both shapes.
Then: compare A and A'.
Then: name the move.
Last: check.
Answer
dilation = scale factor ½