Question

Polygon q is a scaled copy of polygon p. Given that one side in polygon p is 4 and its corresponding side in q is 3, and another side in polygon p is x, and its corresponding side in q is y, if the value of x is 6, what is the value of y? What is the scale factor?

a) 4; 1.5
b) 3; 0.75
c) 2; 1.5
d) 9; 0.75

Answer 1

The value of y in polygon q is 4.5, given a side of length x is 6 in polygon p, and the corresponding scaled sides are 3 in q and 4 in p. The scale factor from p to q is 0.75.

Step-by-step explanation:

A student asks about finding the value of y and the scale factor when scaling between two polygons, given the side lengths in each. To find these, we look at the given ratios and set up a proportion. With sides of length 4 in polygon p and 3 in polygon q, and another side of length x (which is 6) in p and y in q, we can find the scale factor by dividing the sides of q by the corresponding sides of p. So, the scale factor is 3/4, which is 0.75.

To find the value of y, we apply the scale factor to side length x (which is 6):

scale factor = q/p
3/4 = y/6

Cross-multiply and divide to find y:
y = (3/4) * 6
y = (3*6)/4
y = 18/4
y = 4.5

So the value of y is 4.5, and the scale factor is 0.75.