2761.11 – A Sum of Slopes

Tags:Problem Set 5Algebra/TrigonometryGeometry-Euclidean

Suppose the base of an equilateral triangle is on the xx-axis. What is the sum of the slopes of all three sides of the triangle?


Set up the triangle as in the figure below. We know m1 =0m_1 = 0. Note that m2 = b/am_2 = b/a, and m3 =b/am_3 = -b/a. We don't need to know what aa and bb are. Clearly, m1 + m2 + m3 =0m_1 + m_2 + m_3 = 0.