Question

11. *

Quadrilateral ABCD has the following vertices: A(1, 4), B(6,4), C(1, -3), and D(-4, -3).
A dilation centered at the origin with a scale factor of 8 is applied to ABCD to form
A'B'C'D'. Which of the following statements is true?
O A) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same area.
B) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same perimeter.
C) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same side lengths.
D) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same angle measures.

Answer 1

D) Quadrilateral ABCD and quadrilateral A'B'C'D' have the same angle measures.

Explanation:

A dilation basically just means that the shape gets proportionately larger (see attached file).

A cannot be true because of the dilation. The shape is now larger than it was by a factor of eight. Therefore the area will not be the same.

B and C are also not true for basically the same reasons. Shape is bigger, therefore the length of the sides are longer and the perimeter is larger.

The only thing that is not affected by a dilation are the shapes angle measures. If those were affected, A'B'C'D' would not be a dilation of ABCD.

Hope this helps.