Distance and Midpoints: verify that d(A,M)=d(M,B)=(1/2)d(A,B

[Gretta99]

I'm not quite sure how to set this problem up.

d=distance
"M is the midpoint of A and B. Find the indicated point. Verify that d(A,M)=d(M,B)=(1/2)d(A,B)"
M=(2.5,3.5),B=(12,10),A=?

I tried the circle equation...
(x-2.5)^2+(y-3.5)^2=r^2
(12-2.5)^2+(10-3.5)^2=r^2
9.5^2+6.5^2=r^2
132.5=r^2
sqrt(132.5) =sqrt(r^2)
sqrt(132.5)=r

But I'm not sure if that helps me at all in reaching what A is. Am I on the right track? I considered trying to plug the information in to that equation they gave me, but I'm not sure if that's to check my answers or something like that, and if I am supposed to use that equation (even just to check my work afterwards) where do I plug the numbers into?

Thanks,

Michelle

 

[stapel]

Why are you trying to find the square of the distance between M and some point (x, y)...? Instead, maybe you might try plugging the given information into the Midpoint Formula they gave you, and finding the information they asked for...?

Eliz.