Question

Please help! Triangle ABC is translated by the rule (x + 1, y + 1) and then dilated by a scale factor of 2 centered at the origin. Which statement describes the properties of triangles ABC and A''B''C'' after the transformations?

A) ∠C and ∠C'' are congruent after both the translation and the dilation.
B) ∠C and ∠C'' are congruent after the dilation, but not after the translation.
C) segment AC and segment A double prime C double prime are congruent after both the translation and the dilation.
D) segment AC and segment A double prime C double prime are congruent after the dilation, but not after the translation.

Answer 1

A

Explanation:

1) Translated figures are congruent ones, so
`\bigtriangleup ABC\cong \bigtriangleup A'B'C'`, one unit to the right and one up in comparison to
`\bigtriangleup ABC\cong \bigtriangleup ABC`.

2)Since
`\bigtriangleup A''B''C''` was dilated with a scale factor of two then It's a similar figure to
`\bigtriangleup ABC`. Similar figures have congruent angles and different sizes.

Hence, ∠C≅∠C"