Question

ABC has vertices of A(0, 0), B(–4, 0), and C(–2, 4). The coordinates of each vertex are multiplied by 3 to create AEF. Determine if ABC is similar to AEF. Explain your answer.

A. No, they are not similar because the corresponding angles are not congruent.
B. No, they are not similar because the corresponding sides are not proportional.
C. Yes, they are similar with a scale factor of 1:3.
D. Yes, they are similar with a scale factor of 0:3.

Answer 1

Option C is right

Explanation:

Given that ABC has vertices of
`A(0, 0), B(–4, 0), and C(–2, 4).`

When coordinates are multiplied by 3, to create AEF, we get new coordinates as

`A(0,0) B(-12,0) and C(-6,12)`

Comparing the sides we have

`AB = 4 and A'B' =12\\AC=\sqrt (4+16) = 2\sqrt 5\\A'C' =\sqrt (36+144) = 6\sqrt 5`

`BC= \sqrt (4+16) = 2\sqrt 5\\B'C' =\sqrt(36+144) = 6\sqrt 5`

Thus we find that Sides of ABC are proportional to A'B'C'

Hence they are similar with scale factor of 3

Option C is right.

Answer 2

That statement that determine if ABC is similar to AEF and base on the data and the vertices in the given problem. The statement that best describe the two triangle is letter C. Yes, they are similar with a scale factor of 1:30. I hope you are satisfied with my answer.