Question

A line through the origin has a slope of 1 / 3. Carlos thinks the slope of a perpendicular line at the origin will be 3.

Do you agree? Explain why or why not.

Answer 1

Carlos is incorrect.

Explanation:

We have been given that a line through the origin has a slope of
`(1)/(3)`. Carlos thinks the slope of a perpendicular line at the origin will be 3.

We know that the slope of a perpendicular line to a given line is always negative reciprocal of the slope of the given line.

The slope of the perpendicular line at the origin will be negative reciprocal of
`(1)/(3)`.

Let us find negative reciprocal of
`(1)/(3)` as:

`-(1)/((1)/(3))=-(1\cdot 3)/(1)=-3`

Since the slope of a perpendicular line at the origin is
`-3`, therefore, Carlos is incorrect.