Dilate (2, -1) by scale factor 3

Step by step

The question

Question: dilate the point P(2, −1) by scale factor 3.

1 Draw the shape

Put the point on the grid.

2 Multiply each point

Scale factor 3 makes the shape 3 times as big.

Every number is multiplied by 3.

We call the new point P prime.

The little mark means: the new P.

P is (2, −1).

3 times 2 is 6.

3 times −1 is −3.

So P' is (6, −3).

Careful!

A dilation multiplies.

Adding 3 would slide the shape, not make it bigger.

3 The new point

So the image is P'(6, −3).

4 Check

Let's check P.

Draw a line from O through P to P'.

From O to P: right 2, down 1.

From O to P': right 6, down 3.

That is 3 times the moves to P.

So P' is on the same line from O, 3 times as far.

Right!

Let's look back.

First: draw the shape.

Then: multiply each point.

Then: the new point.

Last: check.