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 
