The equations of two of the sides of triangle ABC are x+2y=8 and 2x+y=1. Given that A is the point (2,-3) and that angle ABC=90 degrees, find:

Question

a) the equation of the third side

b) the coordinates of the point B.

Answer 1

x+2y=8 has slope=-1/2 y=-x/2 +4

2x+y=1 has slope -2, y=-2x +1

to be a right triangle

3rd equation must have a negative inserve slope =2 or 1/2

such as y=2x -7

angle ABC is between sides with equations having negative inverse slopes, vertex ABC = (4.4, 1.8)

another vertex ACB = (-2,5)

definitely draw at least a rough graph to see if the solution makes sense. Plot the points and draw the lines