Question 664966
Perpendicular lines have a negative reciprocal slope.
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First, find the slope of the line through (5, -2) and (-3, 14)
slope = {{{(14-(-2))/(-3 - 5) = (16/-8) = -2}}}
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The negative reciprocal slope for the perpendicular line is {{{1/2}}}
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Using the slope and the coordinates (7, 9), solve for y-intercept following
y=mx+b
9 = {{{1/2}}}7 + b
b = 9 - {{{1/2}}}7 = {{{18/2}}} - {{{7/2}}} = {{{11/2}}}
The linear equation for the perpendicular line that passes through (7, 9) is:
{{{highlight(y = (1/2)x + (11/2))}}}
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Red line --> line through (5, -2) and (-3, 14)
Green line --> perpendicular line through (7, 9)
{{{graph(300,200,-10,10,-10,10,-2x+8, (1/2)x+(11/2))}}}
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