Triangle in the Cartesian Plane
Source:
June 8, 2009
analytic geometrygeometry
Problem Statement
The vertices of triangle have coordinates as follows: where and are positive. The origin and point lie on opposite sides of . The area of triangle may be found from the expression:
(A)\ \frac{ab \plus{} ac \plus{} bc \plus{} cd}{2} \qquad
(B)\ \frac{ac \plus{} bd \minus{} ab}{2}\qquad
(C)\ \frac{ab \minus{} ac \minus{} bd}{2}\qquad
(D)\ \frac{ac \plus{} bd \plus{} ab}{2}\qquad
(E)\ \frac{ac \plus{} bd \minus{} ab \minus{} cd}{2}