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

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What is the orthocenter of a triangle with corners at $(2, 4)$ $(2 ,4 )$ , $(1, 3)$ $(1 ,3 )$ , 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 $= m_{b c} = \frac{5 - 3}{3 - 1} = 1$ $= m_(bc) = (5-3) / ( 3-1) = 1$

Slope of CA $= m_{c a} = \frac{5 - 4}{2 - 1} = 1$ $= m_(ca) = (5 - 4) / (2 -1) = 1$

Slope of AB $= m_{a b} = \frac{3 - 4}{1 - 2} = 1$ $= m_(ab) = (3 - 4) / ( 1 - 2) = 1$

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 $(2, 4)$ $(2 ,4 )$ , $(1, 3)$ $(1 ,3 )$ , and (3 ,5 )#?

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

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Explanation:

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