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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