Question

Segment E prime F prime has endpoints located at E′(1, 0) and F′(1, 3). segment EF was dilated by a scale factor of one half from the origin. Which statement describes the pre-image?

segment EF is located at E (0.5, 0) and F (0.5, 1.5) and is half the size of segment E prime F prime.
segment EF is located at E (1, 0) and F (1, 3) and is the same size as segment E prime F prime.
segment EF is located at E (2, 0) and F (2, 6) and is twice the size of segment E prime F prime.
segment EF is located at E (3, 0) and F (3, 9) and is three times the size of segment E prime F prime.

Answer 1

Answer: EF is located at E(2,0) and F(2,6) and is twice the size of E'F'

Reason

The scale factor 1/2 = 0.5 was applied to go from E to E'(1,0)

To go in reverse, we take the reciprocal of 0.5 to get 1/0.5 = 2. Instead of halving, we're doubling the coordinates.

That's how E ' (1,0) turns into E(2,0) and how F ' (1,3) turns into F(2,6)

To verify, take half of E(2,0) to end up with E ' (1,0) again. Do a similar thing with F(2,6) as well to get to F ' (1,3).

Because we doubled the coordinates, the pre-image segment is twice as long compared to the image segment.