What is the orthocenter of the triangle with two altitudes given by the lines x = -1 and y = x+1

(-1,0)



Explanation:

A quick method is to simply look at the graph and notice the two altitudes cross at (-1,0)



A longer method involves a bit of algebra but its not too bad

y = x+1
y = -1+1 ... plug in x = -1 (ie replace x with -1)
y = 0
So when x = -1, the value of y is y = 0
They pair up to get (x,y) = (-1,0) which confirms what the graph is showing

The answer is a (-3,-10.75