Mathematics, 24.07.2019 15:00 caro70

How do you know if two line segments are perpendicular? a. the slope of one is the negative of the slope of the other. b. their slopes are reciprocals. c. their slopes are negative reciprocals. d. their slopes are equal.

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Answer from: wowihavefun

The correct option is

Step-by-step explanation: We are given to select the correct reason for two line segments to be perpendicular.

We know that

If two line segments are perpendicular, then the product of their slopes is - 1.

Let, m and n represents the slopes of two lines that are perpendicular to each other.

Then, we must have

$m\times n=-1\\\\\\\Rightarrow m=-\dfrac{1}{n}~~~~~\textup{and}~~~~~n=-\dfrac{1}{m}.$

This implies that m is the negative reciprocal of n and n is the negative reciprocal of m.

Thus, the slopes are negative reciprocals.

Option (C) is CORRECT.

Answer from: janiyagoldsmith

If two line segments are perpendicular their slopes are negative reciprocals. Option (C) is correct.

Further explanation:

Given:

The options are as follows,

A. The slope of one is the negative of the slope of the other.

B. Their slopes are reciprocals.

C. Their slopes are negative reciprocals.

D. Their slopes are equal.

Explanation:

Consider the slope of the first line as ${m_1}.$

The slope of the second line is ${m_2}.$

The product of the slopes of the perpendicular line is -1.

$\begin{aligned}{m_1} \times {m_2} &= - 1 \\{m_1} &= \frac{{ - 1}}{{{m_2}}}\\\end{aligned}$

The slopes are negative reciprocals to each other.

If two line segments are perpendicular their slopes are negative reciprocals. Option (C) is correct.

Option (A) is not correct.

Option (B) is not correct.

Option (C) is correct.

Option (D) is not correct.

Learn more:

Learn more about inverse of the function . Learn more about equation of circle . Learn more about range and domain of the function

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: line segment, perpendicular, slope, negative slope, reciprocals, slopes are equal, negative reciprocals, graph function, numbers, slope, slope intercept, equation, origin.

Answer from: Quest

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i hope that this ! : d

"stay and stay proud! " - zalgo

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Answer from: Quest

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like, however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

$\bf e(\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad f(\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-2}{)}\implies \implies \cfrac{-2}{0+2}\implies \cfrac{-2}{2}\implies -1 \\\\[-0.35em] ~\dotfill$

$\bf d(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad f(\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{)}{)}\implies \cfrac{0+1}{0+2}\implies \cfrac{1}{2} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~ef}{-1\implies \cfrac{-1}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{-1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{1}\implies 1}}$