Question

ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Find the orthocenter of ABC? explain step by step please.

Answer 1

To find the orthocenter of a triangle, you need to find the point at which the lines, created to be perpendicular to one side of the triangle and passing through the 3rd point intersect.

So for example Side AB has a slope of (6-6)/(4-0) which equals 0. Therefore a line that is perpendicular to Side AB has the inverse opposite sign of the slope, -1/0 which is a vertical line. So the vertical line that goes through point C is x=1

Do the same with another side. Side BC has a slope of (6-3)/(4-1) which equals 1. A line perpendicular to side BC has slope -1/1, which equals -1. Solve for the line with slope -1 that goes through A.

y=-1x+z
6=-1*0+z
z=6
so y=-1x+6

So we have 2 lines x=1 and y=-1x+6

They intersect at (1,5)