Problem 3


A triangle has two of its vertices at  and in a Cartesian coordinate system.  Its third vertex is on the axis.  If the area of the triangle is 2 square units, what are the possible coordinates for this third vertex?


[Problem submitted by Juergen Pahl, LACC Professor of Mathematics.]




Solution for Problem 3:


















Equation of Line 1:  

Equation of Line 2:  


Point of intersection: 

                                                and then  


         Equation 1


Area of the triangle 

                                  =           Equation 2


Substitute Equation 2 into Equation 1:





Solve this equation: or                                  


We get the two possible solutions: