SOLUTION: What is orthocenter of points A(0,10) B(4,10) C(-2,4)

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Question 934028: What is orthocenter of points A(0,10) B(4,10) C(-2,4)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Find the midpoints.
Midpoint of AB : (2,10)
Midpoint of BC :
x%5BBC%5D=%284-2%29%2F2=1
y%5BBC%5D=%2810%2B4%29%2F2=7
Midpoint of AC :
x%5BAC%5D=%280-2%29%2F2=-1
y%5BAC%5D=%2810%2B4%29%2F2=7
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.
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From the diagram, it looks like the orthocenter will be (0,7).
We definitely know that from the midpoint of BC to the midpoint of AC, the equation of the line is y=7.
The line from C to the midpoint of AB is,
y-4=%28%284-10%29%2F%28-2-2%29%29%28x-%28-2%29%29
y-4=%283%2F2%29%28x%2B2%29
y-4=%283%2F2%29x%2B3
y=%283%2F2%29x%2B7
Since we already know y=7
7=%283%2F2%29x%2B7
%283%2F2%29x=0
x=0
(0,7)