Question

If a 50% horizontal scale factor decrease and a 75% vertical scale factor increase were applied to the rectangle above, what would be the new horizontal and vertical measurements? A) horizontal 8 inches; vertical 35 inches B) horizontal 8 inches, vertical 30 inches horizontal 10 inches; vertical 16 inches D) horizontal 12 inches: vertical 28 inches

Answer 1

We have the following rectangle

We want to calculate the new dimensions by applying the corresponding factors.

First we start with the horizontal side. The initial length of this side is 16. Since we are decreasing by a factor of 50% we must subtract 50% to the original length. We can calculate the 50% by multiplying 16 by 50/100. So we get

`16\text{ - }(50)/(100)\cdot16=16\cdot(1\text{ -0.5)=16}\cdot0.5=8`

So the horizontal dimension after scaling is 8.

Now, for the vertical dimension, we are applying a 75% increasing scale factor. So we should add to the original length an 75% extra. To calculate the 75%w e multiply the original length by 75/100. So we get

`20+20\cdot(75)/(100)=20\cdot(1+0.75)=20\cdot(1.75)=35`

so the vertical dimension after scaling is 35.

This leads that the correct answer is A.