Question

Line m passes through points (6, 8) and (2, 1). Line n passes through points (9, 10) and (2, 6). Are line m and line n parallel or perpendicular?

Answer 1

Explanation:

lets calculate each of the gradients(m & n)

for m; x1 = 6,x2 = 2,y1 = 8,y2 = 1

`gradient = (y2 \\ - y1)/(x2 - x1)`

`m = (1 \\ - 8)/(2 - 6) = ( - 7)/( - 4)`

`m = (7 \\ )/(4)`

now lets calculate the gradient for m

x1=9, x2=2, y1=10, y2=6

`n = ( \\ 6 - 10)/(2 - 9)`

`n = ( - 4 \\ )/( - 7)`

`n = (4 \\ )/(7)`

for parallelism

m1 = m2

`(4)/(7 \\ ) = (7)/(4)`

therefore it is not parallel

for perpendicularism

`( - 1 \\ )/( (4)/(7) ) = ( - 7)/(4)`

`( - 1)/( (7)/(4) ) = - ( 4)/(7)`

therefore it is perpendicular