Question

Triangle DEF was dilated according to the rule DO,One-third(x,y)(one-third x, one-third y) to create similar triangle D'E'F'.

On a coordinate plane, (0, 0) is the center of dilation. Triangle F D E is dilated to create smaller triangle F prime D prime E prime. Triangle F D E has points (negative 9, 3), (negative 9, 9), (negative 6, 6). Triangle F prime D prime E prime has points (negative 3, 1), (negative 3, 3), and (negative 2, 2).

Which statements are true? Select three options.

∠F corresponds to ∠F'.
Segment EE' is parallel to segment FF'.
The distance from point D' to the origin is One-third the distance of point D to the origin.
The measure of ∠E' is One-third the measure of ∠E.
△DEF △D'E'F

Answer 1

True:
- ∠F corresponds to ∠F' (dilation preserves angle correspondence).
- The distance from D' to the origin is one-third the distance from D to the origin (scale factor 1/3 from the origin).
- △DEF ∼ △D'E'F' (dilation produces a similar triangle).

False:
- Segment EE' is parallel to segment FF' (EE' and FF' lie on different rays through the origin, so not parallel).
- The measure of ∠E' is one-third the measure of ∠E (dilation preserves angle measures, it does not scale them).