Question

Find the coordinates of the point which divides the line segment joining the
points (4, -3) and (8, 5) in the ratio 3:1 internally

Answer 1

Answer:

Find the coordinates of the point dividing the line segment PQ joining

P(1, -2) and Q(-3, 4) internally in the ratio 1 : 2

Answer 2

Let P(x, y) be the required point. Using the section formula

$\boxed{\sf P(x, y) = \bigg(\dfrac{m_{1} x_{2} + m_{2}x_{1}}{m_{1} + m_{2}}, \dfrac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}\bigg)}$

we get

$\sf x = \dfrac{3(8) + 1(4)}{3 + 1} = \dfrac{28}{4} = 7$

$\sf y = \dfrac{3(5) + 1(-3)}{3 + 1} = \dfrac{12}{4} = 3$

∴ P(x, y) = (7, 3) is the required point