Question

Point P is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of P A is 2 and the length of P B is 3. The Length of A A prime is 4 and the length of B B prime is 5.
Is triangle A'B'C' a dilation of triangle ABC? Explain.

Yes, it is an enlargement with a scale factor of 3.
Yes, it is an enlargement with a scale factor of Eight-thirds.
No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.

Answer 1

No. For a dilation from center P the same scale factor k must satisfy PA' = k·PA, so AA' = |k − 1|·PA and BB' = |k − 1|·PB. Here AA'/PA = 4/2 = 2 but BB'/PB = 5/3 ≈ 1.67, which are not equal, so there is no single k. Thus the points are not moved proportionally from P.