Question

Given vertices a(-2,0), b(4,0), c(3, 5), find the coordinates of the orthocenter?

Answer 1

To find the coordinates of the orthocenter, we need to find the intersection point of the altitudes of the triangle. The coordinates of the orthocenter are (3, -19).

Step-by-step explanation:

To find the coordinates of the orthocenter, we need to find the intersection point of the altitudes of the triangle. The altitude of a triangle is a line segment perpendicular to the opposite side and passing through the vertex.

First, we find the slopes of the lines AB and AC using the formula (y2 - y1) / (x2 - x1). The slope of AB is 0, and the slope of AC is 5/7.

Next, we find the equations of the perpendicular lines passing through B and C. The equation of the line passing through B is y = -7x + 28, and the equation of the line passing through C is y = -7x + 26.

Finally, we solve the system of equations formed by the two perpendicular lines to find the coordinates of the orthocenter. The solution is x = 3 and y = -19. Therefore, the coordinates of the orthocenter are (3, -19).