Question

which of the following sets of slopes represents perpendicular lines? a. 5 and -1/5 b. 0 and ∞ c. 2 and -2 d. 1 and 1

Explanation:

Step1: Recall perpendicular - slope rule

For two non - vertical lines with slopes $m_1$ and $m_2$, they are perpendicular if $m_1\times m_2=- 1$. A horizontal line (slope $m = 0$) and a vertical line (undefined slope, often informally thought of as $\infty$) are also perpendicular.

Step2: Check option a

Calculate the product of the slopes: $5\times(-\frac{1}{5})=-1$.

Step3: Check option b

A horizontal line with slope $m_1 = 0$ and a vertical line (whose slope is undefined, can be thought of as approaching $\infty$ in a non - rigorous sense) are perpendicular.

Step4: Check option c

Calculate the product of the slopes: $2\times(-2)=-4
eq - 1$.

Step5: Check option d

Calculate the product of the slopes: $1\times1 = 1
eq-1$.

Answer:

A. 5 and $-\frac{1}{5}$
B. 0 and $\infty$