Question 1091708
By inspection, we see that the base of the triangle formed by the vertices (-2,-1) and (6,-1) is symmetric about the line x=2,
so this altitude goes through the point (2,-1), and we know the x coordinate of the orthocentre is 2.
To find the y coordinate, we use the fact that an altitude will be perpendicular
to the line formed by any two vertices, and will pass through the 3rd vertex.
Using (6,-1) and (2,5), the line is
y + 1 = ((5+1)/(2-6)(x - 6) -> y = -3/2x + 8
And, since perpendicular lines have negative reciprocal slope, the line for the altitude is 
y + 1 = 2/3(x + 2) -> y = 2/3x + 1/3
The intersection point of x = 2 and y = 2/3x + 1/3 gives the orthocentre
y = 2/3*2 + 1/3 = 5/3
Ans: (2,5/3)