What is the orthocenter of a triangle with corners at #(5 ,7 )#, #(4 ,3 )#, and (1 ,2 )#?

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Answer 1 · 2016-03-23T09:19:17

orthocenter #(79/11, 5/11)#

Solve for the equations of the altitudes and then solve for their intersection

by point-slope form

#y-2=-1/((7-3)/(5-4))(x-1)" "#equation of the altitude thru (1,2)

#y-3=-1/((7-2)/(5-1))(x-4)" "#equation of the altitude thru (4,3)

Simplifying these equations we have
#x+4y=9#
#4x+5y=31#

Simultaneous solution results to

#x=79/11# and #y=5/11#

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