Question

Which statement about polygon PQRST and its image after dilation, polygon P'Q'R'S'T', is correct?

The length of diagonal PS and diagonal P'S' are in the ratio 1:3.
The lengths of side PT and side R'Q' are in the ratio 1:3.
The length of side PT is equal to the length of side P'T'.
The measures of angle S and angle S' are in the ratio 1:3.

Answer 1

The length of diagonal PS and diagonal P'S' are in the ratio 1:3.

Explanation:

Comparing the coordinates of the vertices,

P(0, -3)→P'(0, -9); Q(3, -2)→Q'(9, -6); R(3, 1)→R'(9, 3); S(0, 2)→S'(0, 6); T(-2, 0)→T'(-6, 0)

We can see that the pre-image points have been multiplied by a scale factor of 3. This means comparing the pre-image sides to the image sides, the ratio is 1:3. However, we must compare corresponding sides; the only choice comparing corresponding sides with a ratio of 1:3 is PS to P'S'.