Andrew and Shawn are making kite. They start by drawing their plan onto some squared paper. The initial points that they use are O(0,0), A(7,24) and B(25,0). Andrew says that the fourth vertex of the kite should be on the line that is through (0,0) and perpendicular to the line AB. Find the equation of this line.

Question

Andrew and Shawn are making kite. They start by drawing their plan onto some squared paper. The initial points that they use are O(0,0), A(7,24) and B(25,0). Andrew says that the fourth vertex of the kite should be on the line that is through (0,0) and perpendicular to the line AB. Find the equation of this line.

Answer 1

AB has slope -24/18 = -4/3

so, our line has slope 3/4
Since it passes through (0,0), its equation is

y = 3/4 x

Extra credit:
3/4 x intersects AB at (16,12), and that's the midpoint of the line we want. So, the 4th vertex of the kite is (32,24)