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.

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