A triangle has corners A, B, and C located at #(4 ,2 )#, #(3 ,4 )#, and #(6 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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Answer 1 · 2017-12-02T12:39:20

Length of altitude (CD) passing through point C #= 4.4721#

Equation of side AB
#(y-2)/(4-2) = (x-4) / (3-4)#
#-1( y-2) = 2 (x-4)#
#2x + y = 10#. Eqn (1)

Let Slope of side AB be ‘m’
#m = (4-2) / (3-4) = -2#
Slope of perpendicular line to AB is #= -(1/m) = -(1/-2) = 1/2#

Eqn of Altitude(CD) to AB passing through point C is
#(y-8) =(1/2)(x-6)#
#2y- 16 = x - 6#

#x - 2y = -10#. Eqn (2)

Solving Eqns (1) & (2) we get the base of the altitude (CD) passing through point C.

Solving the two equations, we get
#x=2, y=6#

Length of the altitude passing through point C
#= sqrt((6-2)^2 + (8-6)^2) = sqrt(16 + 4) = 4.4721#

Length of Altitude (CD) passing through point C = 4.4721#

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