A triangle has corners A, B, and C located at #(5 ,2 )#, #(2 ,5 )#, and #(8 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

1 Answer
Binayaka C.
Jun 9, 2016

End points of Altitude CD are #(8,4)# and #(11/2,3/2)#
Length of Altitude #sqrt50/2#

Explanation:

Let CD be the altitude drawn perpendicular to line AB of the triangle from point C. The slope of line AB # (5-2)/(2-5)=3/-3=-1 :.# the slope of altitude CD is #(-1)/(-1)=1#(condition of perpendicularity). The equation of line AB is #y-2= (-1)(x-5) = 5-x or y+x = 7 (1)# The equation of line CD is #y-4= 1(x-8) =x-8 or y-x = -4 (2)# Solving equation (1) & (2) we get #x=11/2 ; y= 3/2# So end points of Altitude CD are #(8,4)# and #(11/2,3/2)# Length of Altitude # sqrt((8-11/2)^2+(4-3/2)^2)=sqrt(25/4+25/4)=sqrt50/2#[Ans]

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