SOLUTION: angle ABC has vertices A(4,4), B(-1,4), and C(1,6). Find the orthocenter of angle ABC

Algebra ->  Triangles -> SOLUTION: angle ABC has vertices A(4,4), B(-1,4), and C(1,6). Find the orthocenter of angle ABC       Log On


   

Question 549170: angle ABC has vertices A(4,4), B(-1,4), and C(1,6). Find the orthocenter of angle ABC
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
AB is the horizontal line y=4, so the altitude from point C is the perpendicular (vertical) line through C, x=1.
The slope of BC is %286-4%29%2F%281-%28-1%29%29=2%2F%281%2B1%29=2%2F2=1, so the slope of the (perpendicular) altitude from/through A is -1%2F1=-1. The altitude is on the line
y-4=%28-1%29%28x-4%29 ---> y-4=-x%2B4%29 ---> y=-x%2B8
The intersection of those two altitudes is the intersection of the 3 altitudes, the orthocenter. It's coordinates are x=1 and y=-1%2B8=7
The orthocenter of triangle ABC is (1,7).