untchick04tm

2022-01-02

Let $y=\left[\begin{array}{c}7\\ 8\end{array}\right]$ and $y=\left[\begin{array}{c}6\\ 8\end{array}\right]$. Compute the distance from y to the line through u and the origin

Andrew Reyes

Expert

Equation of line through u and origin is
$y={y}_{1}=m\left(x-{x}_{1}\right)$ where m is slope
$y-{y}_{1}=\frac{\left({y}_{2}-{y}_{1}\right)}{\left({x}_{2}-{x}_{1}\right)}\left(x-{x}_{1}\right)$
here ${x}_{1}$ and ${y}_{1}$ is (0,0) the line passing through origin

$\left(y-0\right)=\frac{8}{6}\left(x-0\right)$

$⇒-4x+3y=0$
$Ax+By+C=0$
and point y is $\left[\begin{array}{c}7\\ 8\end{array}\right]$ is (7,8)
Now we know distance of point
$d=\frac{|A{x}_{1}+B{y}_{1}+c|}{\sqrt{{A}^{v}+{B}^{v}}}$
$=\frac{4}{5}$

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