Mathematics: Draw a line perpendicular to the line that contains the points (1, 8) and (4, 6) and passes through the point (−2, 8)

Draw a line perpendicular to the line that contains

salihanegawo

11.03.2022

$y=\frac{3}{2} x+\frac{20}{3}$

Step-by-step explanation:

First, to find the original line, employ the slope formula.

$\frac{y2-y1}{x2-x1} \\\\\frac{6-8}{4-1} \\\\\frac{-2}{3}$

The slope of your original line is $-\frac{2}{3}$ .

Next, plug in your slope and the third point to the point-slope formula.

$y-y1=m(x-x1)\\\\y-8=-\frac{2}{3} (x+2)\\\\y-8=-\frac{2}{3} x-\frac{4}{3}\\\\y=-\frac{2}{3} x+\frac{20}{3}$

To find the line which is perpendicular to the line, take the opposite reciprocal of the slope.

To find the opposite, flip the sign. $-\frac{2}{3}$ is negative, so it will become $\frac{2}{3}$ , which is positive.

To find the reciprocal, flip the fraction. $\frac{2}{3}$ would become $\frac{3}{2}$ .

Your slope for the perpendicular line is $\frac{3}{2}$ , so your line is:

$y=\frac{3}{2} x+\frac{20}{3}$

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