MathDB

Triangle in the Cartesian Plane

Source:

November 11, 2005

geometryanalytic geometrygraphing linesslopevectorparallelogramAMC

Problem Statement

Triangle

ABC

lies in the Cartesian Plane and has an area of 70. The coordinates of

B

and

C

are

(12,19)

and

(23,20)

, respectively, and the coordinates of

A

are

(p,q)

. The line containing the median to side

BC

has slope

-5

. Find the largest possible value of

p+q