I need help with the following question. All that I have done so far is drawn a picture and thought about using the triple product of A, B, and C but I am not sure how to complete this. Thanks for any help. Here's the question:
A triangle ABC in the plane has vertices at the points A = (12, 13), B = (-12, -5) and C = (-8, -7).
Let the line AP be perpendicular to BC and meet BC at the point P.
Let the line BQ be perpendicular to CA and meet CA at the point Q.
Let the line CR be perpendicular to AB and meet AB at the point R.
Prove that the three lines AP, BQ and CR meet at a point S and determine the four points P, Q, R and S.
A triangle ABC in the plane has vertices at the points A = (12, 13), B = (-12, -5) and C = (-8, -7).
Let the line AP be perpendicular to BC and meet BC at the point P.
Let the line BQ be perpendicular to CA and meet CA at the point Q.
Let the line CR be perpendicular to AB and meet AB at the point R.
Prove that the three lines AP, BQ and CR meet at a point S and determine the four points P, Q, R and S.