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The vertices of triangle ABC are A(1,3), B(7,7) and C(9,3) and I need to find the orthocenter.

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asked Oct 27, 2015 in GEOMETRY by anonymous

1 Answer

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Step 1:

The vertices of triangle ABC are   and .

Orthocenter:  Orthocenter of a triangle is the pont of intersection of all the altitudes of the triangle.

Orthocenter of a Triangle

Slope of the line passing through the points  and  is .

Find the slope of the side  passing through   and .

.

Observe the figure:  and  are perpendicular.

If  and  are the slopes of two perpedicular lines then .

Slope of the altitude  is .

Find the line equation of the altitude .

Point-slope form of line equation is .

image.

Step 2:

Find the slope of the side  passing through  and .

.

Observe the figure:  and  are perpendicular.

Find the line equation of the altitude .
Slope of the altitude  is image.

Point-slope form of line equation is .

image

image.

Solve (1) and (2) to find the orthocenter.

From (2): image.

Substitute image in (1).

image
Substitute image in image

image

image.

Orthocenter is image.

Solution:

Orthocenter is image.

answered Oct 28, 2015 by cameron Mentor
edited Oct 28, 2015 by cameron

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