Chapter: Co-ordinate Geometry· Mathematics Part 2 (Geometry)
Answer: P(1, 3)
Let \(A(x_1, y_1) = (-1, 7)\), \(B(x_2, y_2) = (4, -3)\), \(m : n = 2 : 3\) and \(P(x, y)\).
By section formula,
\(x = \dfrac{mx_2 + nx_1}{m + n} = \dfrac{2(4) + 3(-1)}{2 + 3} = \dfrac{8 - 3}{5} = \dfrac{5}{5} = 1\)
\(y = \dfrac{my_2 + ny_1}{m + n} = \dfrac{2(-3) + 3(7)}{2 + 3} = \dfrac{-6 + 21}{5} = \dfrac{15}{5} = 3\)
\(\therefore\) Co-ordinates of P are (1, 3).