Question

Triangle EFG is dilated by a scale factor of one half centered at (1, 1) to create triangle E'F'G'. Which statement is true about the dilation?

- The slope of segment EF is the same as the slope of segment E prime H prime.

- segment E prime G prime will overlap segment EG.

- segment GF and segment G prime F prime both pass through the center of dilation.

- segment EF ≅ segment E prime F prime.

Answer 1

segment GF and segment G prime F prime both pass through the center of dilation.

Explanation:

Answer 2

- segment GF and segment G prime F prime both pass through the center of dilation.

Explanation:

The center of dilation (1, 1) is the same point that vertex F, then, both F and F' are located at (1, 1).

G is located at (-2, 1). After the dilation by a scale factor of one half, G' is located at (-0.5, 1), so that the distance between G' and F' is half the distance between G and F. Therefore, segment GF and segment G'F' both pass through the center of dilation.