Step by step
The question
Question: translate the shape A(−2, 1), B(1, 1) and C(−2, 4) by the vector (3, −2).
1 Draw the shape
Put the points on the grid and join them.
2 Read the move
A vector tells the move: across first, then up.
vector (3, −2) means right 3, down 2.
Right 3 means x gets 3 bigger: x + 3.
Down 2 means y gets 2 smaller: y − 2.
So every point (x, y) goes to (x + 3, y − 2).
3 Move each point
Start at A.
Go right 3.
Then go down 2.
We land on the new point.
We call the new point A prime.
The little mark means: the new A.
A is (−2, 1).
Right 3: −2 plus 3 is 1.
Down 2: 1 minus 2 is −1.
So A' is (1, −1).
Careful!
Down makes y smaller.
So we take 2 away.
We do not add it.
Now B: 1 plus 3 is 4.
1 minus 2 is −1.
So B' is (4, −1).
Now C: −2 plus 3 is 1.
4 minus 2 is 2.
So C' is (1, 2).
4 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(1, −1), B'(4, −1) and C'(1, 2).
5 Check
Let's check.
Draw an arrow from each point to its new point.
All the arrows are the same: the same length, the same way.
So the shape slid, without turning.
Right!
Let's look back.
First: draw the shape.
Then: read the move.
Then: move each point.
Then: draw the image.
Last: check.