SOLUTION: the vertices of a triangle ABC are A(2,1) and B(6,-1) and C(4,11).find the equation of altitude through A of triangle ABC

Question 758661: the vertices of a triangle ABC are A(2,1) and B(6,-1) and C(4,11).find the equation of altitude through A of triangle ABC

Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Find the gradient of BC
Formula: y2 - y1/x2 - x1
11-(-1)/4 - 6
12/-2
-6
As an altitude is at right angles
to the line it emerges from, the
gradient of the line BC and the
gradient of the altitude will
multiply together to give -1
m1 x m2 = -1
So, if the gradient of BC is -6
then the gradient of the altitude
is 1/6.
Setting up the equation:
Using y - b = m(x - a) with m = 1/6 Coords of A (2,1)
y - 1 = 1/6(x - 2)
y - 1 = 1/6x - 2/6
y = 1/6x - 2/6 + 6/6 (1)
y = 1/6x + 4/6
This is the equation but you can
multiply through by 6
6y = x + 4
Hope this helps.
:-)
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