Question

Find the orthocenter of a triangle with vertices at each set of coordinates: (0,0), (6,4), (4,8)

a) (3, 3)
b) (5, 6)
c) (2, 5)
d) (4, 6)

Answer 1

The coordinates of the orthocenter of the triangle with vertices at (0,0), (6,4), and (4,8) are (2,5). Hence the correct answer is option C

Step-by-step explanation:

The orthocenter of a triangle is the point where the altitudes of the triangle intersect. To find the orthocenter of a triangle with vertices at (0,0), (6,4), and (4,8), we need to first find the equations of the altitudes.

The equations of the altitudes are found by taking the slope of a side of the triangle and then finding the equation of the line passing through the midpoint of that side and perpendicular to it. This process is repeated for each side of the triangle.

After finding the equations of the altitudes, we solve the system of equations to find the point of intersection, which is the orthocenter of the triangle.

The coordinates of the orthocenter for this triangle are (2,5).

Hence the correct answer is option C