Question 1104478
 ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter, including any necessary points or slopes you had to derive. 
Could someone really help me on this?
The graph is not needed since I can sketch it myself. I just need help with the steps that need to be taken in order to find the orthocenter. 
Thank You So Much!
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You need to find the three altitudes of the triangle.
Example::
Using base A(0,6) B(4,6) 
slope = (6-6)/(4-0) = 0 
So, the base is horizontal
Therefore the altitude is vertical and passes thru C(1,3)
The equation of the altitude must be x = 1
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Using base A(0,6) C(1,3)
slope = (6-3)/(0-1) = -3
So the altitude must have slope = +1/3 and it must pass thru B(4,6)
Find the equation of that altitude::
Form y = mx + b
Solve for "b":: 6 = (1/3)4 + b
b = 14/3
The equation of that altitude must be y = (1/3)x + 14/3
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Find the equation of the 3rd altitude.
Then find the intersection of the three altitudes.
That point is the orthocenter.
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Cheers,
Stan H.
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