How do i find the orthocenter of the triangle with these coordinates(8,10)(5,-10)(0,0)

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.

Find the equation of 2 of the line segment, then find the perpendicular lines to them, then solve for x by making the perpendicular equations equal

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.