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?

Question

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?

Caroline Aucoin · Accepted Answer

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 Find the other altitude endpoint by solving for it. #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 Concurrent resolution #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# May God bless you all. I hope this explanation helps.

Parker Allen · Answer

undefined The altitude going through corner C has endpoints (4, 8) and (5/3, 11/3). Its length is √13/3 ≈ 1.52 units.