Question

50 POINTS!! Triangle ABC with vertices A(4, −6), B(2, −8), and C(−10, 4) is dilated by a scale factor of 2 to obtain triangle A′B′C′. Which statement best describes triangle A′B′C′?

A) It is similar to triangle ABC and has coordinates A′(2, −3), B′(1, −4), and C′(−5, 2).
B) It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8).
C) It is congruent to triangle ABC and has coordinates A′(2, −3), B′(1, −4), and C′(−5, 2).
D) It is congruent to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20,

Answer 1

B) It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8).

Explanation:

If the vertices of a triangle ABC are dilated by a scale factor of 2, the coordinates of the vertices of triangle A'B'C' can be found by multiplying each coordinate of ABC by the scale factor.

Therefore, the coordinates of the vertices of triangle A'B'C' are:

• A' = (4 × 2, -6 × 2) = (8, -12)
• B' = (2 × 2, -8 × 2) = (4, -16)
• C' = (-10 × 2, 4 × 2) = (-20, 8)

As the triangle has been dilated, its size has changed but its shape has not. Therefore, the triangles are similar.