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
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
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