(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

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.

Step-by-step explanation:

Let the points of a triangle be

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.

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:

The graph of the image coordinates attached below.

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