A triangle has corners A, B, and C located at #(3 ,5 )#, #(2 ,1 )#, and #(4 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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Answer 1 · 2016-03-22T11:45:47

The other endpoint is #(64/17, 137/17)#
#l=1/17sqrt(17)=0.2425#

#y-1=4(x-2)# equation of the line containing A and B
#y-8=-1/4(x-4)# equation of the line containing C and perpendicular to line AB

Solve for the other endpoint of the altitude

#y=4x-7" "# equation of the line containing A and B after simplification

#x+4y=36" "#equation of the line containing C and perpendicular to line AB after simplification

Simultaneous solution

#x+4(4x-7)=36" "#
#17x=36+28#
#17x=64#
#x=64/17#

#y=4x-7#
#y=4(64/17)-7#
#y=(256-119)/17#
#y=137/17#

The other endpoint is #(64/17, 137/17)#

the length #l#

#l=sqrt((64/17-x_c)^2+(137/17-y_c)^2)#

#l=sqrt((64/17-4)^2+(137/17-8)^2)#

#l=sqrt(((64-68)/17)^2+((137-136)/17)^2)#

#l=sqrt(((-4)/17)^2+((1)/17)^2)#

#l=sqrt(((-4)/17)^2+((1)/17)^2)#
#l=1/17sqrt(17)=0.2425#

God bless....I hope the explanation is useful.