For , the vertices are , and . In terms of , , and , find the coordinates of the orthocenter of . (The orthocenter is the point of concurrence for the altitudes of a triangle.)
The coordinates of the orthocenter of in terms of , , and with the vertices , and .
The triangle with vertices , and .is shown in the above figure.
Let , , be the altitudes of the triangle .
The point of intersection of the altitudes is the orthocentre.
If two lines are perpendicular, then the product of their slopes is or one slope is negative reciprocal of the other slope.
(i.e.) If , then or
Since is the horizontal line, slope is zero.
Obviously the altitude is vertical and it has the equation,
The slope of the line with vertices and is as follows.
Using the slope formula and choosing , , , and
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