Question

Which line is perpendicular to a line that has a slope of 1/2 ?

a.) line AB
b.) line CD
c.) line FG
d.) line HJ

Answer 1

Option D. line HJ

Explanation:

Slope of line AB which passes through points A(-4, -2) and B(4, 2)

`m1=(2+2)/(4+4)=(4)/(8)=1/2`

m1 = 1/2

Slope of line CD passing through C(-4, 0) and D(4, -4)

`m2=(0+4)/(-4-4)=(4)/((-8))=-(1)/(2)`

m2 = -1/2

Slope of the line HJ passing through H(-1, 3) and J(1, -1)

`m3 =(-1-3)/(1+1)=(-4)/(2)=(-2)`

m3 = (-2)

As we know that two line will be perpendicular if their m×m' = -1

Here we see that Line AB is having slope m1 = 1/2 and slope of HJ is m3 = (-2)

m1×m3 = (1/2)×(-2) = -1

Which clearly tells us that line HJ is perpendicular to line AB.

Therefore Option D. is the correct option.