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:

 

                            or