Final answer:
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.