1. In the xy-coordinate plane, point A is the midpoint of the segment with endpoints (2,4) and (-4,-4). What is the distance from point A to the origin?

Question

I know how to find the distance between the two points- 10. But I don't know where to go from there.

2. The radius of circle B is 125 percent of the radius of circle A, and the radius of circle C is 80 percent of the radius of circle B. If the area of circle A is 50pi, what is the area of circle C?

Thanks in advance!

Answer 1

well, you need to find the midpoint. That is at the average of the ends: (-1,0). Now just find the distance from there to (0,0).

If the radii are a,b,c we have

b = 5/4 a
c = 4/5 b = 4/5 * 5/4 a = a
so, the radii are the same, and hence the areas as well.

Note that we don't even have to remember that the areas scale as the square of the radii.

Answer 2

How do you find the "average of the ends"? What does that mean and how do you get -1?