Question

True or false. If two lines are perpendicular, their slopes are negative reciprocals.

Answer 1

this is true.

for example, if line a has a slope of 1/2 then line b (which is perpendicular) has a slope of -2.

Answer 2

True

Explanation:

Let there be two perpendicular lines AB and CD having slope m₁ and m₂.

Now, we know that,

When two lines are perpendicular, the product of their slopes is -1.

Thus, we get that the product of m₁ and m₂ is -1.

i.e. m₁ × m₂ = -1

i.e.
`m_(1)=(-1)/(m_(2))`

i.e. m₁ is negative reciprocal of m₂.

Thus, the slope of line AB is negative reciprocal of the slope of line CD.

Hence, the given statement is true.