Tell whether the orthocenter of the triangle with the given vertices is inside, on, or outside the triangle. Then find the coordinates of the orthocenter. G(1, 6), H(5, 6), J(3, 1)

Answer 1

The orthocenter is the intersection of the altitudes of the triangle.

To do this problem:

Calculate the slope of 2 sides of the triangle.

The slope of the altitude to that side will be the negative reciprocal of that slope.

Use the point slope form to write the equation of the altitude to the opposite vertex.

Write the equations in slope-intercept form and set them equal to each other.

The solution is the x co-ordinate of the orthocenter. Use either of the 2 equations to find the y co-ordinate.

Use graph paper to plot the triangle and its orthocenter.