The dilation of ΔABC by a scale factor of 2 with a center of dilation at (-4,-9). A (-4,-6), B (3,-6), and C (-2,-1). What is the coordinate of C'?

The coordinate of C' is (0,7).

Step-by-step explanation:

Relative coordinates of each point of the ABC-Triangle are obtained first:

Where:

- Absolute coordinates of the vertices of the ABC-Triangle.

- Coordinates of the center of dilation.

- Relative coordinates of the vertices of the ABC-Triangle.

If , , and , the relative coordinates are now computed:

Each outcome is consequently dilated:

The absolute coordinates of A', B' and C' are, respectively:

The coordinate of C' is (0,7).

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have