Question

A school principal is mapping out some new features for a triangular playground. He sketches the playground on grid paper. The coordinates of the vertices of the playground are (1, 10), (−5, 2), and (7, 2). The principal wants to put monkey bars at the orthocenter of the playground. What are the coordinates of the monkey bars? (__,__)​

Answer 1

To find the coordinates of the orthocenter of a triangle, you need to intersect the altitudes of the triangle. The coordinates of the orthocenter for the given triangle are (1, 4).

Step-by-step explanation:

To find the coordinates of the orthocenter of a triangle, you need to intersect the altitudes of the triangle. The altitude is a perpendicular line drawn from a vertex to the opposite side of the triangle.

Step 1: Find the slopes of the sides of the triangle using the given coordinates.

Step 2: Find the point of intersection of the altitudes by finding the equations of the altitudes and solving them simultaneously.

Step 3: The coordinates of the orthocenter are the coordinates of the point of intersection found in Step 2.

In this case, the coordinates of the orthocenter are (1, 4).