Question

FAN AND MEDAL!!
3 points lie on an xy plane, with each point representing where a particular person lives. Amy lives at point (2,3); Brian lives at point (0,7); and Claire lives at point (-2,3). They all wish to meet up with each other for lunch, but at a location that is equidistant from each of their respective houses. At what point do they meet?
a. (0,4.5)
b. (0,13/3)
c. (0,3)
d. (1,5)
e. (-1,5)

Answer 1

The way you do this is to graph those points and look at what you think is the point equidistant between what looks to be the center of the triangle and your three "houses". To me it looks like (0, 5) is the center, but that is not one of your choices. The next closest is the point (0, 4.5). So the way you find out if 4.5 is the midpoint between all the houses, use the distance formula to find the distance between each house and the point (0, 4.5). If all three distances come out the same, (0, 4.5) is equidistant from all 3 houses. Get it? I'm going to do this, but I'd like to hear what you come up with as well. Start by graphing your points on a piece of graph paper.

Answer 2

It does come out that the midpoint between the three houses (vertices) is (0, 4.5).

Answer 3

thanks