What is the orthocenter of a triangle with corners at #(2 ,4 )#, #(1 ,3 )#, and (3 ,5 )#?

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What is the orthocenter of a triangle with corners at #(2 ,4 )#, #(1 ,3 )#, and (3 ,5 )#?

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Answer 1 · 2018-01-13T12:37:53

Triangle doesn’t exist as the slopes of the three sides are equal; I.e. the three points are collinear

Explanation:

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Slope of BC #= m_(bc) = (5-3) / ( 3-1) = 1#

Slope of CA #= m_(ca) = (5 - 4) / (2 -1) = 1#

Slope of AB #= m_(ab) = (3 - 4) / ( 1 - 2) = 1#

As may be seen, all the three sides of the triangle have their slopes equal; i.e. the three points are collinear. That shows such a triangle can’t exist.

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What is the orthocenter of a triangle with corners at #(2 ,4 )#, #(1 ,3 )#, and (3 ,5 )#?

1 Answer

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