Find-the-equation-of-the-perpendicular-bisector-of-the-line-joining-the-points-5-4-to-the-point-9-3-

Question Number 8243 by lepan last updated on 04/Oct/16

F i n d t h e e q u a t i o n o f t h e p e r p e n d i c u l a r b i s e c t o r o f t h e l i n e j o i n i n g t h e p o i n t s (- 5, 4) t o t h e p o i n t (9, - 3)

Answered by sandy_suhendra last updated on 04/Oct/16

let A (- 5, 4) and B (9, - 3)

P is midpoint of AB so P (\frac{- 5 + 9}{2}, \frac{4 - 3}{2}) = P (2, \frac{1}{2})

the gradient of AB = m_{AB} = \frac{y_{A} - y_{B}}{x_{A} - x_{B}} = \frac{4 + 3}{- 5 - 9} = - \frac{1}{2}

the gradient of the perpendicular bisector = m_{1}

so m_{AB} \times m_{1} = - 1

- \frac{1}{2} \times m_{1} = - 1

m_{1} = 2

the equation of the perpendicular bisector :

y - y_{P} = m_{1} (x - x_{P})

y - 2 = 2 (x - \frac{1}{2})

y = 2 x + 1