Question 661700: Hi,
I'm having a difficult time solving the following problem:
Point P lies on the perpendicular bisector of segment ST. If S has coordinates (5,14), T has coordinates (-3,2), and P has coordinates (-a/2,a), what is the value of a?
Any assistance would be greatly appreciated.
Thank you!
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
Point P lies on the perpendicular bisector of segment ST.
If S has coordinates (5,14), T has coordinates (-3,2)
Midpoint segment ST
(5,14),
(-3,2) Midpoint = (1,8) and slope m = (14-2)/(5-(-3)) = 12/8 = 3/2
Point P(-a/2,a) lies on the perpendicular bisector: slope -2/3
(-a/2,a)
(1, 8) slope m = 
| Cross Multiplying to solve
-6(a-8) = -2(a+2)
-6a + 48 = -2a - 4
52 = 4a
13 = a
and...
(-13/2,13)
( 1 , 8) 
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