Find the coordinates of the point P, which divides the join of A \left(\right. - 2 , 5 \left.\right) and B \left(\right. 3 ,

Engineering

Mathematics

Section Formulae and Centres of a Triangle

Question

Find the coordinates of the point

P

, which divides the join of

A (- 2, 5)

and

B (3, - 5)

in the ratio

2 : 3

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Let

P (x, y)

divide the line

A (- 2, 5)

and

B (3, - 5)

in the ratio

2 : 3

Using section formula,

(x, y) = (\frac{m x_{2} + n x_{1}}{m + x}, \frac{m y_{2}}{x y_{1}} m + x)

where

m = 2, n = 3, x_{1} = - 2, y_{1} = 5, x_{2} = 3, y_{2} = - 5

P (x, y) = (\frac{2 \times 3 + 3 \times - 2}{2 + 3}, \frac{2 \times - 5 + 3 \times 5}{2 + 3})

= (\frac{6 - 6}{5}, \frac{- 10 + 15}{5}) = (0, \frac{5}{5})

= (0, 1)

∴

The point

(0, 1)

divides the line

A B