Question

What must be true to prove that q ⊥ n?

A. The slope of q must be the reciprocal of the slope of n.
B. The slope of q must be the negative reciprocal of the slope of n.
C. The slope of q must be the slope of n multiplied by –1.
D. The slope of q must be the slope of n multiplied by –1n.

Answer 1

Answer:

B

Step-by-step explanation:

TO prove that q is perpendicular to n they must have a slope that's an opposite reciprocal to each other. For example the slope for q could be -5 first you must flip the equation so now its -1/5 then you change the sign to positive so now it's 1/5. Opposite meaning change sign reciprocal meaning flip the fraction.

Answer 2

We need to find the true statement among the given statements.

The correct option is B. The slope of q must be the negative reciprocal of the slope of n.

It is given that $q\perp n$

For two lines to be perpendicular the product of the slopes is $-1$

Let $m_1$ be the slope of $q$ and $m_2$ be the slope of $n$.

So, if $q\perp n$

$m_1m_2=-1\\\Rightarrow m_1=\dfrac{-1}{m_2}$

So, The slope of q must be the negative reciprocal of the slope of n.

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