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Triangle ABC is defined by the points A(3,8), B(7,5), and C(2,3).
Create an equation for a line passing through point A and perpendicular to BC.

Sagot :

abidemiokin

The required equation for a line passing through point A and perpendicular to BC is 2y + 5x = 31

First, we need to get the slope of the line perpendicular to BC

  • Given the coordinates B(7,5), and C(2,3)

Get the slope BC:

[tex]m_{BC} = \frac{3-5}{2-7}\\m_{BC}=\frac{-2}{-5}\\m_{BC}=\frac{2}{5}\\[/tex]

The slope of the line perpendicular to BC will be -5/2

The slope of the required line in point-slope form is expressed as;

[tex]y-y_0=m(x-x_0)\\[/tex]

Given the following

m = -5/2

(x0, y0) = (3, 8)

Substitute into the formula:

[tex]y-8=-5/2(x-3)\\2(y-8)=-5(x-3)\\2y - 16=-5x+15\\2y+5x=15+16\\2y+5x=31\\[/tex]

Hence the required equation for a line passing through point A and perpendicular to BC is 2y + 5x = 31

Learn more here: https://brainly.com/question/17119045

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