Question

Find the equations of perpendicular bisectors of sides of the triangle whose vertices are P(-1, 8), Q(4, – 2) and R(- 5, – 3).

Answer 1

Let A, B and C be the midpoints of sides PQ, QR and PR respectively of APQR. A is the midpoint of side PQ.

Slope of perpendicular bisector of PQ is 1/2 and it passes through (3/2), 3).

Equation of the perpendicular bisector of side PQ is

∴ 2y + 5 = -18x – 9 

∴ 18x + 2y + 14 = 0 

∴ 9x + y + 7 = 0 C is the midpoint of side PR

∴ 11(2y – 5) = – 8 (x + 3) 

∴ 22y – 55 = – 8x – 24 

∴ 8x + 22y -31 = 0