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)
