Answer:
Carlos is incorrect.
Step-by-step explanation:
We have been given that a line through the origin has a slope of [tex]\frac{1}{3}[/tex]. 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 [tex]\frac{1}{3}[/tex].
Let us find negative reciprocal of [tex]\frac{1}{3}[/tex] as:
[tex]-\frac{1}{\frac{1}{3}}=-\frac{1\cdot 3}{1}=-3[/tex]
Since the slope of a perpendicular line at the origin is [tex]-3[/tex], therefore, Carlos is incorrect.
