Polygon pqrst shown below is dilated with a scale factor of 3, keeping the origin as the center of dilation:
which statement about polygon pqrst and its image after dilation, polygon p'q'r's't', is correct?
a) the length of diagonal ps and diagonal p's' are in the ratio 1: 3
b) the length of diagonal pt and diagonal r'q' are in the ratio 1: 3
c) the length of diagonal pt is equal to the length of side p't'.
d) the measure of angle s and angle s' are in the ratio 1: 3.

A) The Length Of Diagonal PS And Diagonal P'S' Are In The Ratio 1:3

Step-by-step explanation:

when a polygon is multiplied or scaled by k, a constant scalar number to form another polygon then these two polygons are similar. And similar polygons have proportional lengths of corresponding sides. Ratios within the polygons sides will be equal to the corresponding sides ratios of the other polygons.  The corresponding sides of image are scalar multiple of preimage

x'=kx

where x' is side in image

x is side in preimage

and k is scalar number

so the ratio between these two corresponding side will be 1:3

In given case as the scalar factor k is 3 so the ratio between corresponding sides will be 1:3.

Hence option A is correct:The Length Of Diagonal PS And Diagonal P'S' Are In The Ratio 1:3!

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