HMMT 二月 2007 · GEN2 赛 · 第 2 题
HMMT February 2007 — GEN2 Round — Problem 2
题目详情
- [ 2 ] A parallelogram has 3 of its vertices at (1,2), (3,8), and (4,1). Compute the sum of all possible x coordinates of the 4th vertex.
解析
- [ 2 ] A parallelogram has 3 of its vertices at (1,2), (3,8), and (4,1). Compute the sum of all possible x coordinates of the 4th vertex. Answer: 8 . There are three possibilities: the 4th vertex must be opposite one of the three given vertices. These three possibilities have as a medial triangle the three given vertices, so the sum of their x coordinates is the same as the sum of the x coordinates of the given triangle.