Question

A triangle has vertices at A(-2, 4), B(-2, 8), and C(6, 4). If it has coordinates of (-0.25, 0.5) after the triangle has been dilated with a center of dilation about the origin, which statements are true? Check all that apply.

a. The coordinates of A are (0.75, 0.5).
b. The scale factor is 2.
c. The coordinates of B are (-0.25, 1).
d. The scale factor is 8.

Answer 1

Only one statement is correct: the scale factor is 8. After applying this scale factor to the original coordinates of the triangle's vertices, we can understand that the other statements about specific coordinates after dilation are incorrect.

Step-by-step explanation:

To determine whether the given statements are true following the dilation of the triangle with vertices at A(-2, 4), B(-2, 8), and C(6, 4), we need to calculate the scale factor of the dilation and apply it to the original coordinates. Since we have a post-dilation coordinate of (-0.25, 0.5), we will compare this with the original coordinates to determine the correct scale factor and the resulting coordinates.

Let's analyze each statement:

The scale factor is 8: We use the original and given post-dilation coordinates to check this. A proper calculation would show that the scale factor would indeed lead to the coordinates given, suggesting this statement is correct.

Accordingly, none of the statements concerning the coordinates of A and B after dilation are correct, while the statement regarding the scale factor being 8 is true.