Step by step
The question
Question: describe the move that takes A(1, 1), B(3, 1) and C(1, 4) to A'(4, −1), B'(6, −1) and C'(4, 2).
A(1, 1), B(3, 1) and C(1, 4)
A'(4, −1), B'(6, −1) and C'(4, 2)
1 Draw both shapes
Put the shape on the grid
and its image.
2 Compare B and B'
Look at what happened to the numbers of B: B(3, 1) went to B'(6, −1).
B(3, 1) → B'(6, −1)
x went from 3 to 6: plus 3.
x: 3 → 6 is + 3
y went from 1 to −1: minus 2.
y: 1 → −1 is − 2
On the grid: right 3
then down 2.
3 Name the move
So the rule is: (x, y) goes to (x + 3, y − 2).
(x, y) → (x + 3, y − 2)
Careful!
A translation moves every point the same way.
So check more than one point.
Careful: every point moves the same way
So the move is a translation: right 3, down 2.
translation = right 3, down 2
4 Check
Let's check the rule on the other points.
A goes to (4, −1).
That is A'.
A(1, 1) → (4, −1) = A'
C goes to (4, 2): C'.
Right!
C(1, 4) → (4, 2) = C'
Let's look back.
First: draw both shapes.
Then: compare B and B'.
Then: name the move.
Last: check.
Answer
translation = right 3, down 2