Question

find the coordinates of the orthocenter. write your answer as an ordered pair.
15
(grid with a triangle, axes labeled x and y, grid lines, points at (4,4), (8,4), (8,6))

Explanation:

Step1: Identify the triangle type

The triangle has a right angle (since one side is horizontal and another is vertical). In a right - angled triangle, the orthocenter is at the vertex of the right angle.

Step2: Find the right - angle vertex

Looking at the coordinates of the vertices: Let's assume the vertices are $(4,4)$, $(8,4)$ and $(8,6)$. The side between $(8,4)$ and $(8,6)$ is vertical (same x - coordinate) and the side between $(4,4)$ and $(8,4)$ is horizontal (same y - coordinate). So the right - angle is at the point $(8,4)$.

Step3: Confirm the orthocenter

For a right - angled triangle, the orthocenter coincides with the vertex of the right angle. So the orthocenter has coordinates $(8,4)$.

Answer:

$(8, 4)$