Question 1019014: An altitude of a triangle is a line drawn from a vertex of the triangle perpendicular to the opposite side of the triangle. Find the equation of the altitude drawn from A(0,0) to the side formed by B(3,4) and C(5,-2).
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
Gradient (Slope) of BC = y2 - y1/x2 - x1
= -2 -4/5 - 3
= -6/2
= -3
Lines at right angles to one another
have gradients (slopes) that multiply
together to give -1
m1 x m2 = -1
-3 x m2 = -1
m2 = 1/3
This is the gradient of the altitude.
Using line equation
y - b = m(x - a)
with m = 1/3 and A (0,0) = (a,b)
y - 0 = 1/3(x - 0)
y = 1/3x
This is the equation of the altitude
Hope this helps :-)
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