Question

Using a scale factor of 5/2, angle ABC is dilated from the origin to form angle XYZ. What are the coordinates of X and Z?

A) X(0, 0), Z(0, 0)
B) X(5, 2), Z(0, 0)
C) X(0, 0), Z(5, 2)
D) X(5, 2), Z(5, 2)

Answer 1

The coordinates of X after dilation would remain at the origin (0, 0). Without the original coordinates of point B, precise coordinates for Z cannot be determined, but they would be the original coordinates of B multiplied by the scale factor of 5/2.

Step-by-step explanation:

When dilating an angle from the origin using a scale factor, the coordinates of the new angle are found by multiplying the coordinates of the original angle by the scale factor. For angle ABC dilated to form angle XYZ with a scale factor of 5/2, assuming point A is at the origin, point X would remain at the origin (because anything times zero is zero), so X(0, 0).

Assuming point B corresponds to point Z and without the specific coordinates of B, it is impossible to determine the exact coordinates of Z. However, the coordinates of Z would be proportional to point B's coordinates multiplied by the scale factor of 5/2. Therefore, only the coordinates of X are definitely known.

The answer is C) X(0, 0), Z(5, 2) assuming B was originally at (2, 1). However, as the question doesn't provide exact coordinates for B, this is an assumption, and the exact coordinates for Z cannot be determined without the original coordinates of B.