SOLUTION: Determine the coordinates of the orthocentre of triangle DEF with vertices at D (-3,4) E (8,-2) F (4,5)

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Question 1137650: Determine the coordinates of the orthocentre of triangle DEF with vertices at D (-3,4) E (8,-2) F (4,5)
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

given: with vertices at
(,)
(,)
(,)

the orthocenter: the point where the three "altitudes" of a triangle meet
find the slopes of the lines that contain segments and
slope of
now, we need a slope of perpendicular line, altitude to segments :
slope of perpendicular line, altitude : ->
(substitute , , )






equation of the altitude to :


slope of
altitude to : ->
(substitute , , )




equation of the altitude to :


intersection of the altitudes will be orthocenter
equation 1:
equation 2:
Solving for and :








The coordinates are (, ). This is the orthocenter.





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