SOLUTION: Please help me! I need to find the coordinates of midpoint P of line segment BC. Then calculate the lengths of AP, BP, and CP. The diagram can be found here: http://i.imgur.com/S7X

Algebra ->  Triangles -> SOLUTION: Please help me! I need to find the coordinates of midpoint P of line segment BC. Then calculate the lengths of AP, BP, and CP. The diagram can be found here: http://i.imgur.com/S7X      Log On


   

Question 899047: Please help me! I need to find the coordinates of midpoint P of line segment BC. Then calculate the lengths of AP, BP, and CP. The diagram can be found here: http://i.imgur.com/S7XQH1B.jpg
Thanks for the help!
Found 2 solutions by Fombitz, fcabanski:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The midpoint is the average of x and y values of the endpoint.
x%5Bm%5D=%28x%5BB%5D%2Bx%5BC%5D%29%2F2
x%5Bm%5D=%280%2B2h%29%2F2
x%5Bm%5D=h
.
.
.
y%5Bm%5D=%28y%5BB%5D%2By%5BC%5D%29%2F2
y%5Bm%5D=%282k%2B0%29%2F2
y%5Bm%5D=k
(h,k)
.
.
.
AP%5E2=%28h-0%29%5E2%2B%28k-0%29%5E2
AP%5E2=h%5E2%2Bk%5E2
AP=sqrt%28h%5E2%2Bk%5E2%29
.
.
BP%5E2=%28h-0%29%5E2%2B%28k-2k%29%5E2
BP%5E2=h%5E2%2B%28-k%29%5E2
BP=sqrt%28h%5E2%2Bk%5E2%29
.
.
CP%5E2=%28h-2h%29%5E2%2B%28k-0%29%5E2
CP%5E2=%28-h%29%5E2%2Bk%5E2
CP=sqrt%28h%5E2%2Bk%5E2%29

Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
To find the midpoint, average the x and y values of the two points.


P is the midpoint: ((2h+0)/2, (2k+0)/2) = (h,k)


The distance between two points is the square root of: the distance between the x coordinates squared plus the distance between the y coordinates squared.


The length of AP is sqrt%28%28h-0%29%5E2+%2B+%28k-0%29%5E2%29 = sqrt%28h%5E2+%2B+k%5E2%29
You can do the other two using the formula.