Question
M and N are the midpoints of opposite sides of square ABCD.A point is selected at random in the square.find the probability that it lies in traingle ADM but not in triangle ADN
Answers
Reiny
I picked M as the midpoint of AB, and N as the midpoint of DC
let P be the intersection of AN and DM
in triangle ADM but not in triangle ADN
--> triangle AMP
by simple ratio calculations, the area of triangle AMP = (1/8)the square.
so prob(of your event) = 1/8
let P be the intersection of AN and DM
in triangle ADM but not in triangle ADN
--> triangle AMP
by simple ratio calculations, the area of triangle AMP = (1/8)the square.
so prob(of your event) = 1/8