In quadrilateral A B C D , A B → = a → , B C → = b → , D A → = a → - b → , M is the midpoint of B C and X is a point on D M such that D X → = 4 5 D M → . Then the points A , X and C

Step-by-step solution

In ∆ A B C , A B → + B C → = A C → ⇒ A C → = a → + b →         . . . i In ∆ A D C , A D → + D C → = A C → ⇒ D C → = A C → - A D → ⇒ D C → = a → + b → + a → - b → = 2 a → M is the midpoint of B C , so M C → = b → 2 . In ∆ M D C M D → + D C → = M C → ⇒ M D → = b → 2 - 2 a → = b → - 4 a → 2 &