An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(4 ,9 )# to #(8 ,5 )# and the triangle's area is #48 #, what are the possible coordinates of the triangle's third corner?
Coordinates of third corner A of the triangle is
Area = 48
Equation of line passing through point B and having slope 6 is
Slope of altitude h passing through mid point of BC is 1
Mid point of BC is
Equation of altitude h is
Solving Eqns (1) & (2), we get coordinates of point A.
Coordinates of the third corner A is