# Dilation Matrix

How to use the dilation matrix to find the image under a dilation: formula, 1 example, and its solution.

## Formula

### Formula

For the dilation of k,

the dilation matrix is

kI = [k 0 / 0 k].

I: Identity matrix

## Example

### Example

### Solution

The image is under

the dilation of 2.

So write the dilation matrix

2I.

Write the vertex matrix.

A(-2, 1), B(2, 3), C(0, -1)

So the vertex matrix is

[-2 2 0 / 1 3 -1].

So the vertex matrix of the image is

2I[-2 2 0 / 1 3 -1].

I is the identity matrix.

So, by its definition,

I[-2 2 0 / 1 3 -1]

= [-2 2 0 / 1 3 -1].

Multiply 2 to each element.

[-4 4 0 / 2 6 -2]

is the vertex matrix of the image.

So column 1 is the image of A:

A'(-4, 2).

Column 2 is the image of B:

B'(4, 6).

Column 3 is the image of C:

C'(0, -2).

So

A'(-4, 2)

B'(4, 6)

C'(0, -2)

is the answer.

### Graph

This is the graph of △ABC

and its image △A'B'C'.

The image is under the dilation of 2.