△ABC has vertices of A (0, 0), B (4, 4), and C (8, 0). Find the orthocenter of △ABC.

Answer 1

Ortho center:  Ortho center of a triangle is the pont of intersection of all the attitudes of the triangle.

Step 1 find the slope of  sides of triangle

AB , CF are perpendicular.

We know that perpendicular lines slopes are reciprocal to each other.

CF line equation in slope intercept form.

BC , AD are perpendicular.

AD line equation in slope intercept form.

Step 2 Solving two altitude CF , AD  equations

and 

From (1) and (2)

Substitute the x value in equation (2).

Coordinates of ortho center of △ABC is (4, 4 ).