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Find the orthocenter of a triangle with the coordinates (1,0) (4,7) (8,-3)

 Feb 5, 2020
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The orthocenter of the triangle is the point of intersection of the three altitudes.

 

An altitude of a triangle is a line that passes through a vertex and is perpendicular to the opposite side.

 

Label these points:    A = (1,0)     B = (4,7)     C = (8,-3)

 

Find the slope of AB:  slope  =  (7 - 0) / (4 - 1)  =  7/3

Find the slope of AC:  slope  =  (-3 - 0) / (8 - 1)  =  -3/7

 

Since these slopes are negative reciprocals, AB is perpendicular to AC.

Therefore, angle(A) is a right angle.

 

In the special case of a right triangle, the three altitudes intersect at the vertex of the right triangle; in this case, the point (1,0).

 Feb 5, 2020

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