Question

Tell whether the orthocenter is is orthocenter is inside, on, or outside the triangle. Then, find the coordinates of the orthocenter. Q(-1,5) R(4,3) S(-1,-2) I’m having some trouble graphing this problem. I’m on #5. The image is attached .

Answer 1

Firstly, let us look at the meaning of orthocenter of a triangle.

The orthocenter of a triangle is the intersection of the triangle's three altitudes.

An illustartion is shown below

The point H in the figure above is the orthocenter of the triangle above.

Now, for the question given,

The coordinates of the vertices of the triangle are

Q(-1,5) R(4,3) S(-1,-2)

Part A:

Tell whether the orthocenter is inside or outside:

Answer: The orthocenter is inside the triangle

To determine the coordinate of the orthocenter by graphing

Plot a perpendicular line from point R to meet QS

Then plot another perpendicular line from point S to meet QR

The point of intersection of the two lines is the orthocenter

The graph is shown below

The point of intersection of the two perpendicular lines is point (1,3).

Hence, the orthocenter of the triangle is (1, 3)