Which statement about polygon pqrst and its image after dilation, polygon p'q'r's't', is correct?

Asked by maham237 @ in Mathematics viewed by 368 People

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.

Answered by maham237 @


Answer:

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

Step-by-step 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'.


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