Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter, including any necessary points or slopes you had to derive.
The orthocentre is the intersection of the 3 altitudes of the triangle.
From your sketch you can see that AB is horizontal, so the altitude from C
to AB would simply be given by x = 3
All we need is a second altitude, I will find it from A to BC
slope of BC = (6-3)/(4-1) = 3/3 = 1
so the slope of the altitude is -1 and since A(0,6) is a y-intercept
the equation of the altitude is y = -x + 6
but x = 3, so y = -3+6 = 3
the orthocentre is (3,3) , note that is falls outside the circle, which
is totally ok
also notice that Jishka's new "robot answering service" could not
handle this relatively easy problem and did not answer it.
