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.

Answer 1

Answer:

Carlos is incorrect.

Step-by-step explanation:

We have been given that a line through the origin has a slope of $\frac{1}{3}$. 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 $\frac{1}{3}$.

Let us find negative reciprocal of $\frac{1}{3}$ as:

$-\frac{1}{\frac{1}{3}}=-\frac{1\cdot 3}{1}=-3$

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