Step by step
The question
Question: translate the point P(5, −2) by the vector (−3, 4).
1 Draw the shape
Put the point on the grid.
2 Read the move
A vector tells the move: across first, then up.
vector (−3, 4) means left 3, up 4.
Left 3 means x gets 3 smaller: x − 3.
Up 4 means y gets 4 bigger: y + 4.
So every point (x, y) goes to (x − 3, y + 4).
3 Move each point
Start at P.
Go left 3.
Then go up 4.
We land on the new point.
We call the new point P prime.
The little mark means: the new P.
P is (5, −2).
Left 3: 5 minus 3 is 2.
Up 4: −2 plus 4 is 2.
So P' is (2, 2).
Careful!
Left makes x smaller.
So we take 3 away.
We do not add it.
4 The new point
So the image is P'(2, 2).
5 Check
Let's check.
Draw an arrow from each point to its new point.
The arrow goes left 3, up 4.
Right!
Let's look back.
First: draw the shape.
Then: read the move.
Then: move each point.
Then: the new point.
Last: check.