Dilate (-2, 1) by scale factor 2

Step by step

The question

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

1 Draw the shape

Put the point on the grid.

2 Multiply each point

Scale factor 2 makes the shape 2 times as big.

Every number is multiplied by 2.

We call the new point P prime.

The little mark means: the new P.

P is (−2, 1).

2 times −2 is −4.

2 times 1 is 2.

So P' is (−4, 2).

Careful!

A dilation multiplies.

Adding 2 would slide the shape, not make it bigger.

3 The new point

So the image is P'(−4, 2).

4 Check

Let's check P.

Draw a line from O through P to P'.

From O to P: left 2, up 1.

From O to P': left 4, up 2.

That is 2 times the moves to P.

So P' is on the same line from O, 2 times as far.

Right!

Let's look back.

First: draw the shape.

Then: multiply each point.

Then: the new point.

Last: check.