Question

Deciding Which Type of Dilation Is Represented
Explain whether this dilation is an enlargement or a reduction, and how you know.
Triangle A B C is enlarged to triangle A prime B prime C prime.

Answer 1

Short answer: it’s an enlargement — the phrase “enlarged to triangle A′B′C′” means the image is larger than the preimage.

How to tell in general (so you can check any diagram):
- Compute the scale factor k. You can do this either by comparing corresponding side lengths (k = A′B′ / AB = B′C′ / BC = C′A′ / CA) or by comparing distances from the center of dilation to a vertex (k = distance(center,A′) / distance(center,A)).
- If k > 1 the dilation is an enlargement (image bigger). If 0 < k < 1 it is a reduction (image smaller). If k = 1 it is congruent (no size change).
- Another visual check: if every vertex A, B, C and its image A′, B′, C′ lie on rays through a common center and the images lie farther from the center than the originals, it’s an enlargement (closer = reduction).

Example: if AB = 3 and A′B′ = 6 then k = 6/3 = 2 (>1) so it’s an enlargement.