Explained: "Let y=[78] and y=[68]. Compute the distance from..."

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untchick04tm

Answered question

2022-01-02

Let

y = [\begin{matrix} 7 \\ 8 \end{matrix}]

and

y = [\begin{matrix} 6 \\ 8 \end{matrix}]

. Compute the distance from y to the line through u and the origin

Answer & Explanation

Andrew Reyes

Beginner2022-01-03Added 24 answers

Equation of line through u and origin is
$y = y_{1} = m (x - x_{1})$ where m is slope
$y - y_{1} = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})} (x - x_{1})$
here $x_{1}$ and $y_{1}$ is (0,0) the line passing through origin
$x_{2} = 6, y_{2} = 8$
$(y - 0) = \frac{8}{6} (x - 0)$
$y = \frac{4}{3} x 3 y - 4 x = 0$
$\Rightarrow - 4 x + 3 y = 0$
$A x + B y + C = 0$
and point y is $[\begin{matrix} 7 \\ 8 \end{matrix}]$ is (7,8)
Now we know distance of point $(x_{1}, y_{1}) o m A x + b y + C = 0$
$d = \frac{| A x_{1} + B y_{1} + c |}{\sqrt{A^{v} + B^{v}}}$
$= \frac{4}{5}$

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