Question

Polygon P'Q'R'S'T' shown on the grid below is an image of polygon PQRST after dilation with a scale factor of 3, keeping the origin as the center of dilation: Two polygons are drawn on a coordinate grid. Polygon PQRST has vertices at P 0 and negative 3, Q 3 and negative 2, R 3 and 1, S 0 and 2, T negative 2 and 0. Polygon P prime Q prime R prime S prime T prime has vertices at P prime 0 and negative 9, Q prime 9 and negative 6, R prime 9 and 3, S prime 0 and 6, and T prime negative 6 and 0. Which statement about corresponding sides and angles of the two polygons is correct? The measures of angle Q and angle Q' are in the ratio 1:3. The length of side TS is equal to the length of side T'S'. The length of diagonal RT is equal to the length of diagonal R'T'. The lengths of side SR and side S'R' are in the ratio 1:3.

Answer 1

Answer:

D is the answer

Answer 2

Answer:

The correct option is 4. The lengths of side SR and side S'R' are in the ratio 1:3.

Step-by-step explanation:

The vertices of polygon are P(0,-3), Q(3,-2), R(3,1), S(0,2), T(-2,0).

The vertices of image are P'(0,-9), Q'(9,-6), R'(9,3), S'(0,6), T'(-6,0).

It is given that polygon P'Q'R'S'T' is the image of polygon PQRST after dilation with a scale factor of 3. It means both polygons are similar.

The corresponding angles of similar figure and same and the corresponding sides are proportional. It means the sides of image are three times of the corresponding sides of pre-image.

SR and S'R' are corresponding sides.

$S'R'=3\times SR$

$\frac{S'R'}{3}=SR$

$\frac{1}{3}=\frac{SR}{S'R'}$

$1:3=SR:S'R'$

The lengths of side SR and side S'R' are in the ratio 1:3.

Therefore the correct option is 4.