Find the slope of any line perpendicular to the line passing through (1,−2) and (−8,1)

erwachsenc6
2022-10-17
Answered

Find the slope of any line perpendicular to the line passing through (1,−2) and (−8,1)

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toliwask

Answered 2022-10-18
Author has **15** answers

The slope of the line passing through (1,-2) and (-8,1) is = $\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$ or $\frac{1+2}{-8-1}=-\frac{1}{3}$

So the slope of the perpendicular line is $-\frac{1}{-\frac{1}{3}}=3$. Since the condition of perpendicularity of two lines is product of their slopes will be equal to -1

So the slope of the perpendicular line is $-\frac{1}{-\frac{1}{3}}=3$. Since the condition of perpendicularity of two lines is product of their slopes will be equal to -1

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$\begin{array}{cccc}2& 2& 0& 2\\ 0& k& 1& 1\\ 1& 2& k& 2\end{array}$

Would I try to be putting this into Row-Echelon form? I have an inkling by playing with it that $k=-1$ for no solutions and $k=1$ for an infinite number of solutions. I can't do the Gaussian steps properly with a $k$ involved to produce some decent working though.

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I know I want to be using Gaussian Elimination here, I've augmented the matrix and I'm perfectly familiar with ERO's and back-solving for systems without unknown constants but this is new to me.

$\begin{array}{cccc}2& 2& 0& 2\\ 0& k& 1& 1\\ 1& 2& k& 2\end{array}$

Would I try to be putting this into Row-Echelon form? I have an inkling by playing with it that $k=-1$ for no solutions and $k=1$ for an infinite number of solutions. I can't do the Gaussian steps properly with a $k$ involved to produce some decent working though.

Thank you in advance for any help, solutions or tips. :)