SOLUTION: Given triangle ABC with vertices A(6, 3), B(-5, -8), and C(-3, 6), let BP and CQ be the perpendiculars dropped from B and C to their opposite sides of triangle ABC. Find the coordi

Question 1181232: Given triangle ABC with vertices A(6, 3), B(-5, -8), and C(-3, 6), let BP and CQ be the perpendiculars dropped from B and C to their opposite sides of triangle ABC. Find the coordinates of orthocenter H of triangle ABC.
P.S. Can you show full solution, thanks.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Given triangle with vertices
A(, ),
B(, ), and
C(, ),

let BP and CQ be the perpendiculars dropped from B and C to their opposite sides of triangle ABC
a line through is perpendicular to a line through
slope of a line through is

.......use one point to find

a line through is:

then a perpendicular line will have a slope
........use point B

and a perpendicular line is

now we need a line that passes through which is perpendicular to BA
line BA have a slope
......use one point to find

a line that passes through

a line that passes through will have a slope
....use coordinates of C

a line that passes through is

the orthocenter is intersection point of a lines that passes through and

--------------------

the coordinates of orthocenter H of triangle ABC are: (,)

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