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

Foundation

Mathematics Foundation

Coordinate Geometry

section formulae

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

(1, 0)

(1, 1)

(0, 1)

(0, 0)

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Given that

A (- 2, 5) B (3, - 5)

Using section formula (m:n) if ratio, then points are

x = \frac{m x_{2} + n x_{1}}{m + n}

x = \frac{2 \times 3 + 3 (- 2)}{2 + 3}

= \frac{6 - 6}{5}

∴ x = 0

y = \frac{m y_{2} + n y_{1}}{m + n}

y = \frac{2 (- 5) + 3 (5)}{2 + 3}

= \frac{- 10 + 15}{5}

∴ y = \frac{5}{5} = 1

∴ P \to (0, 1)