Answer to Question #138811 in Analytic Geometry for Mohammad Jamshaid

Question

Find the value of k if the line joining (4,k) and (6,8) and the line joining (-1,4) & (0,8) are parallel and perpendicular.

Answer 1

Slope of line joining (4,k) and (6,8) is

(8-k)/(6-4) = (8-k)/2

Slope of line joining (-1,4) and (0,8) is

(8-4)/(0+1) = 4

Two lines having slopes m₁ and m₂ will be parallel if m₁=m₂ and perpendicular if m₁= -1/m₂

So if parallel then (8-k)/2 = 4 => k = 0

If perpendicular then (8-k)/2 = -1/4

=> 16 - 2k = -1 => k = 17/2

Answer

Parallel if k = 0

Perpendicular if k = 17/2 = 8.5