Question

Find the coordinates of the point which divides the line segment joining (- 1, 3) and (4, -7) internally in the ratio 3 : 4.

Answer 1

Let our points be A(-1, 3) and B(4, -7) and required point be C( x, y)

Given that point divides internally in ratio of 3:4. 

By section formula,

x = \(\frac{mx_2 + nx_1}{m + n}\), y = \(\frac{my_2 + ny_1}{m + n}\)

Here, m = 3 and n = 4

∴ x = \(\frac{3\times4\times4\times(-1)}{3 + 4},\) y = \(\frac{3\times(-7) + 4\times3}{3 + 4}\)

∴ x = \(\frac{12 - 4}{7},\) y = \(\frac{-21 + 12}{7}\)

∴ x = \(\frac{8}{7},\)y = \(\frac{-9}{7}\)

Hence, the required point is C\((\frac{8}{7},\frac{-9}7)\)