Question

A ABC A(6, 8); B(3, 4); C(–2, 2) are its vertices. The bisector of ∠A cuts BC at D.

a. Find BD : CD.

b. Find the coordinates of D.

Answer 1

a. \(AB=\sqrt{3^2+4^2}=5\)

\(AC=\sqrt{8^2+6^2}=10\)

AB : AC = 5 : 10 = 1 : 2

b. x coordinate of D = \(3+\frac{1}{3}\times(-2-3)=\frac{4}{3}\)

y coordinate of D = \(4+\frac{1}{3}(2-4)=\frac{10}{3}\)

Coordinates of D \((\frac{4}{3},\frac{10}{3})\)