Question

A need help Dilations-He Said, She Said (12/10)

Answer 1

We conclude that the original triangle ΔDEF is dilated by a scale factor of 5/2 to get the image triangle ΔD'E'F'.

Therefore, 'Cárl' is correct. Hence, option 'a' is correct.

Explanation:

Checking the location of the vertices of the original triangle ΔDEF

• D(-2, 4)
• E(2, 4)
• F(0, 2)

Checking the location of the dilated vertices of the image triangle ΔD'E'F'

• D'(-5, 10)
• E'(5, 10)
• F'(0, 5)

Notice that if we multiply the vertices of the original triangle ΔDEF by 5/2, we get the correct image vertices of image triangleΔD'E'F'

i.e.

D(-2, 4) → D'(5/2 (-2), 5/2 (4)) → D'(-5, 10)

E(2, 4) → E'(5/2 (2), 5/2(4)) → D'(5, 10)

F(0, 2) → E'(5/2 (0), 5/2(2)) → F'(0, 5)

Thus, we conclude that the original triangle ΔDEF is dilated by a scale factor of 5/2 to get the image triangle ΔD'E'F'.

Therefore, 'Cárl' is correct. Hence, option 'a' is correct.