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Question
X(4,9), Y(-5,4) and Z(7,-4) are the vertices of a triangle. Find the equation of the altitude of the triangle through X.
Solution
The altitude through X is perpendicular tp YZ.
Slope of YZ = `(-4 - 4)/(7 + 5) = (-2)/3`
⇒ m = Slope of YZ = `(-2)/3`
Slope line perpendicular to YZ will be `(-1)/"m" = 3/2`
This line passes through X(4,9)
Using the point slope Formulae,
y - y1 = m(x - x1)
y - 9 = `3/2`(x - 4)
⇒ 2y - 18 = 3x - 12
⇒ 2y = 3x + 6
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