Question

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′? (5 points)

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

Answer 1

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

Explanation:

Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).

The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,

A' = 2A

A'(8, -12) = 2×A(4, -6)

These facts are all you need to know to choose the correct answer (shown above).