What is the slope of any line perpendicular to the line passing through $(- 21, 2)$ $(-21,2)$ and $(- 32, 5)$ $(-32,5)$ ?

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What is the slope of any line perpendicular to the line passing through $(- 21, 2)$ $(-21,2)$ and $(- 32, 5)$ $(-32,5)$ ?

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Answer 1 · 2015-12-16T03:40:54

slope of the perpendicular line $= \frac{11}{3}$ $=11/3$

Explanation:

First we need to find the slope of the line passing through the points: $(- 21, 2) and (- 32, 5)$ $(-21, 2) and (-32, 5)$ , the slope $m$ $m$ between the points:
$(x_{1}, y_{1}) and (x_{2}, y_{2})$ $(x_1, y_1) and (x_2, y_2)$ is given by:
$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_2-y_1)/(x_2-x_1)$ , so in this case:
$m = \frac{5 - 2}{- 32 - (- 21)}$ $m=(5-2)/(-32-(-21))$ , simplifying we get:
$m = \frac{3}{- 32 + 21} = \frac{3}{- 11} = - \frac{3}{11}$ $m=3/(-32+21)=3/-11=-3/11$
Now the perpendicular lines have slopes that are negative reciprocals, so if $m_{1} and m_{2}$ $m_1 and m_2$ are the slopes of the two perpendicular lines then:
$m_{2} = - \frac{1}{m_{1}}$ $m_2=-1/m_1$ , therefore in this case:
$m_{2} = - \frac{1}{- \frac{3}{11}} = \frac{11}{3}$ $m_2= -1/(-3/11) = 11/3$

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What is the slope of any line perpendicular to the line passing through $(- 21, 2)$ $(-21,2)$ and $(- 32, 5)$ $(-32,5)$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

What is the slope of any line perpendicular to the line passing through (−21,2)(-21,2) and (−32,5)(-32,5)?

1 Answer

Explanation:

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Impact of this question

What is the slope of any line perpendicular to the line passing through $(- 21, 2)$ $(-21,2)$ and $(- 32, 5)$ $(-32,5)$ ?