A triangle has corners A, B, and C located at #(2 ,3 )#, #(5 ,8 )#, and #(3 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?

1 Answer
Nov 15, 2017

Length of altitude passing through point C is #5.831#

Explanation:

Eqn of line AB is
#(y-y_1) / (y_2-y_1) = (x-x_1)/(x_2-x_1)#
#(y - 3)/(8-3) = (x-2)/(5-2)#
#3y-3 = 5x-10#
#5x-3y = 7#. Eqn (1)

Slope of line AB #=(y_2-y_1) / (x_2-x_1) = (2-3)/(3-2) = -1#
Slope of altitude passing through point C #= -(1/-1) = 1#
Eqn of Altitude passing through point C is
#(y-y_1) = m (x -x_1)#
#y - 2 = 1 * (x - 3)#
#x - y = 1# Eqn (2)

Solving Eqns (1) , (2) we get coordinates of altitude base passing through C.
#2y = 2, y = 1, x = 2#

Length of Altitude passing through C is
# sqrt( ((3+2)^2+(2+1)^2) = sqrt34 = 5.831#