A (0,0), B(8,10), C(5,-10) First, find the slope of AB and AC, slope of AB is 5/4, slope of AC is -2 next, find the negative reciprocals of the slopes: -4/5 and 1/2 respectively so the altitude of AB is a line with a slope of -4/5 passing through (5,-10) the altitude of AC is a line with a slope of 1/2 passing through (8,10) find these two lines: Plug (5,-10) in y=(-4/5)x+b to find b, b=-6, so y=(-4/5)x -6 plug (8,10) in y=(1/2)x +b to find b, b=6, so y=(1/2) x +6
the point where these two lines meet is the orthocenter. y=(-4/5)x -6 y=(1/2) x +6 (-4/5)x -6=(1/2) x +6 x=-120/13 y=(1/2)*(-120/13)+6=18/13 so the orthocenter is (-120/13, 18/13) these numbers look odd, but I've run the vertex through an orthodox calculator, and got the same result.
the bottom left and top right are always going to be negative. The right top and bottom are positive numbers. so the answer is -3'1 for the first top one then the second bottom dot is -6'1
