Olympiad workbookIOQMStraight Lines
Let A B C be a triangle in the x y plane, where B is at the origin (0,0) . Let B C be produced to D such that B C: C D=1: 1, C A be produced to E such that C A: A E=1: 2 and A B be produced to F such that A B: B F=1: 3 . Let G(32,24) be the centroid of the triangle A B C and K be the centroid of the triangle D E F . Find the length G K .
Correct answer
40
Step-by-step solution
B C: C D=1: 1 hence D= (2 x₁, 2 y₁ )C A: A E=1: 2 hence E= (3 x₂-2 x₁, 3 y₂-2 y₁ )A B: B F=1: 3 hence F= (-3 x₂,-3 y₂ ) Centroid of D E F=K=(0,0) Centroid of A B C=G=(32,24) G K= 32^2+24^2 =40