Question

The equations shown represent two altitudes of a triangle. y = x+1 and y = −2x−1 What are the coordinates of the orthocenter of the triangle?

Answer 1

The coordinates of the orthocenter of the triangle is;

(-2/3,1/3)

Explanation:

To find the coordinates of the orthocenter, all we have to do is solve for x and y of the given altitudes

We can get this by solving both equations simultaneously

Simply equate the two y’s

x + 1 = -2x-1

x + 2x = -1-1

3x = -2

x = -2/3

To get y, simply substitute into any of the equation, the value of x

y = -2/3 + 1

y = 1/3