An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(2 ,9 )# and the triangle's area is #18 #, what are the possible coordinates of the triangle's third corner?
There are two possible points at
The solution makes use of the formula for the area of a triangle
positive area for counterclockwise arrangement of points
negative area for clockwise arrangements of points
Let (x_1, y_1) be the unknown point and Let
For the equal sides because the triangle is isosceles, we have
Simultaneous solution using first and second equations results to
There is another point which may be solved by using the negative area
Simultaneous solution using second and third equations results to
God bless....I hope the explanation is useful.