What is the orthocenter of a triangle with corners at #(1 ,1 )#, #(6 ,6 )#, and (4 ,6 )#?

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What is the orthocenter of a triangle with corners at #(1 ,1 )#, #(6 ,6 )#, and (4 ,6 )#?

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Answer 1 · 2016-10-20T21:05:34

The orthocenter is #(1, 9)#

Explanation:

The line segment from point #(6,6)# to #(4, 6)# a horizontal line.
The altitude passing through point #(1,1)# is a vertical line with the equation:

#x = 1#

This will, also, be the x coordinate of the orthocenter.

The slope of the line from point #(1, 1)# to #(6,6)# is clearly 1, then the slope of the altitude is -1. Use point-slope form to force the altitude through point #(4,6)#

#y - 6 = -1(x - 4)#

#y = 10 - x#

Use #x = 1# to find the value of the y coordinate of the orthocenter.

#y = 9#

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What is the orthocenter of a triangle with corners at #(1 ,1 )#, #(6 ,6 )#, and (4 ,6 )#?

1 Answer

Explanation:

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