Question

(0,0) (-4,-4) (2,-4) graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin​

Answer 1

The image coordinates are:

A'(0, 0)

B'(-8, -8)

C'(4, -8)

The graph of the image coordinates attached below.

The image triangle A'B'C' is illustrated in green color.

Explanation:

Let the points of a triangle be

• A(0,0)

• B(-4,-4)

• C(2,-4)

We need to determine the graph of the image of this triangle after a dilation with a scale factor of 2 centered at the origin.

• As scale factor > 0, thus the image will be enlarged.

A dilation by a scale factor of 2 centered at the origin means the coordinates of the image can be obtained by multiplying the original coordinates with 2.

Next, the rule of dilation by a scale factor of 2 is given by

Dilation: (x, y) → (2x, 2y), centered at (0, 0)

P(x, y) → P' (2x, 2y)

A(0, 0) → A' (2(0), 2(0)) → A'(0, 0)

B(-4, -4) → B' (2(-4), 2(-4)) → B'(-8, -8)

C(2,-4) → C' (2(2), 2(-4)) → C'(4, -8)

Therefore, the image coordinates are:

• A'(0, 0)

• B'(-8, -8)

• C'(4, -8)

The graph of the image coordinates attached below.

The image triangle A'B'C' is illustrated in green color.