What is the orthocenter of a triangle with corners at #(2 ,7 )#, #(1 ,1 )#, and (3 ,2 )#?

1 Answer
Apr 26, 2018

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Please read the explanation.

Explanation:

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The altitude of a triangle is a perpendicular line segment from the vertex of the triangle to the opposite side.

The Orthocenter of a triangle is the intersection of the three altitudes of a triangle.

#color(green)("Step 1"#

Construct the triangle #ABC# with

Vertices #A(2, 7), B(1,1) and C(3,2)#

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Observe that #/_ACB = 105.255^@#.

This angle is greater than #90^@#, hence ABC is an Obtuse triangle.

If the triangle is an obtuse triangle, the Orthocenter lies outside the triangle.

#color(green)("Step 2"#

Construct altitudes through the vertices of the triangle as shown below:

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All the three altitudes meet at a point referred to as the Orthocenter.

Since the triangle is obtuse, the orthocenter lies outside the triangle.

#color(green)("Step 3"#

Observe that the Orthocenter has #(4.636, 1.727)# as its coordinates.

Hope it helps.