Question

Find the orthocenter for the triangle described by each set of vertices:Q (3-7), R (9,5), S (9,-9).The coordinates of the orthocenter are ______?

A) (33, -7)
B) (9, 5)
C) (9, -9)
D) (3, -7)

Answer 1

The coordinates of the orthocenter are A) (33, -7).

Step-by-step explanation:

The orthocenter of a triangle is the point of intersection of its altitudes. The altitudes are the perpendiculars drawn from each vertex to the opposite side.

For the given triangle with vertices Q(3, -7), R(9, 5), and S(9, -9):

1. The altitude from Q would be perpendicular to the line RS.

2. The altitude from R would be perpendicular to the line QS.

3. The altitude from S would be perpendicular to the line QR.

Calculating these altitudes and finding their point of intersection, which is the orthocenter, gives the coordinates (33, -7).

Therefore, the correct answer is A) (33, -7).