Question

Which lines are perpendicular ?

Answer 1

Lines C and D

Explanation:

For a pair of lines to be perpendicular ,

the product of their slope must be - 1 .

Slope of A:

`2x - 3y = 6\\\\-3y = -2x + 6\\\\y = (-2x)/(-3) + (6)/(-3)\\\\`

`y = (2)/(3)x - 2\\\\slope_A = (2)/(3)`

Slope of B:

`3x - 2y = - 9\\\\-2y = - 3x - 9\\\\y = (-3x)/(-2) - (9)/(-2)\\\\y =(3x)/(2) + (9)/(2)\\\\slope_B = (3)/(2)`

Slope of C:

`y = - (3)/(2)x - 5 \\\\slope_C = -(3)/(2)`

Slope of D:

`y = (2)/(3)x + 2\\\\slope_D = (2)/(3)`

Product of the slopes = - 1

`slope_A * slope_B = (2)/(3) * (3)/(2) = 1 \\eq - 1 \\\\Therefore, not\ perpendicular.\\\\Slope_B * slope_C = (3)/(2) * (-3)/(2) = (-9)/(4) \\eq -1\\\\Therefore , not \ perpendiucalr.\\\\Slope_C * slope_D = -(3)/(2) * (2)/(3) = - 1\\\\Therefore , perpendicular\\\\\\Slope_A * slope_D = (2)/(3) * (2)/(3) = (4)/(9) \\eq 1\\\\therefore , not \ perpendicular.`