What is the orthocenter of triangle ABC?

Question

The coordinates are A = (0,-2); B = (4,-2); and C = (-2,-8). I need help finding the coordinates of the orthocenter. I have looked on youtube but I'm not completely understanding. Any help would be appreciated!

Answer 1

The orthocenter of a triangle is the point of intersection of the altitudes or heights drawn from each of the three vertices. The height will be perpendicular to the side where it is taken.

A = (0,-2); B = (4,-2); and C = (-2,-8)

so: let's get the slope of a side: AC which will be (-8+2)/(-2-0) =  3, so the slope of the perpendicular is -(1/3) and the equation of the height line from B will be ( y+2) = -(1/3)*(x-4) => (3y+6)= -x+4, then the first equation of a line will be

3y + x = -2

now for the  line from point A to line BC we have slope of BC = (-8+2)/(-2-4) = 1 and the slope of the perpendicular is -1, the equation from the point A will be (y+2) = -(x-0) so the equation is y+x=-2

y+x=-2

solving this two equations because they will have (x,y) as the point where they meet will give to us

y=0 and x = -2, the orthocenter is at (-2,0)

CHECK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!