Question

Orthocenter of the triangle with vertices J(1,0) H(6,0) I(3,6)

Answer 1

(3, 1)

Explanation:

The orthocenter is the point where the altitudes meet. Since all three altitudes meet there, it is only necessary to look at two of them. A graph helps immensely.

In the attached graph, we notice that segment HJ is horizontal, so the x-coordinate of the orthocenter will be that of point I (x=3).

The segment IJ has a rise of 3 for a run of 1, so its perpendicular through point H will have a rise of 1 for a run of -3. That gets you to point (3, 1) from point H, so (3, 1) is the orthocenter.