Consider a triangle with vertices located at P(0, 0), Q(10, 0), and R(0, 14). Determine the coordinates of the orthocenter of this triangle.

The correct answer is (0, 0).

Step 1: Identify the given vertices of the triangle.
The vertices of the triangle are:
P = (0, 0)
Q = (10, 0)
R = (0, 14)

Step 2: Analyze the positions of the vertices on the Cartesian plane.
Vertex P(0, 0) is situated at the origin.
Vertex Q(10, 0) lies along the positive x-axis, meaning line segment PQ lies along the x-axis.
Vertex R(0, 14) lies along the positive y-axis, meaning line segment PR lies along the y-axis.

Step 3: Determine the nature of the triangle.
Since the x-axis and y-axis are perpendicular to each other at the origin, the angle formed between side PQ and side PR is 90°.

$\angle QPR={90}^{\circ }$

Thus, △PQR is a right-angled triangle, right-angled at vertex P(0, 0).

Step 4: Find the orthocenter of the triangle.
The orthocenter of a triangle is the point of intersection of its three altitudes.
In any right-angled triangle, the two perpendicular sides (legs) serve as altitudes to each other. The altitude from vertex Q to side PR is segment QP, and the altitude from vertex R to side PQ is segment RP. These two altitudes intersect directly at the right-angled vertex.
Consequently, the orthocenter of any right-angled triangle always coincides with the vertex containing the right angle.

Therefore, the coordinates of the orthocenter of △PQR are (0, 0).