What are the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2: 3?

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(1,4)

(2,3)

(1,3)

(3,4)

answer is C.

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Detailed Solution

Given that,
The given points are (−1, 7) and (4, −3).
The ratio in which they are divided = 2:3.
We know that if a line joining two points is divided in the ratio m:n by the point P, then its coordinates can be calculated as,

P (x, y) = [m x 2 + n x 1 m + n, m y 2 + n y 1 m + n]

.
Here,

x 1 = − 1 y 1 = 7 x 2 = 4 y 2 = − 3

and m=2 and n=3.
For the x-coordinate,

x = 2 × 4 + 3 × (− 1) 2 + 3 ⇒ x = 8 − 3 5 ⇒ x = 55 ⇒ x = 1

For the y-coordinate,

y = 2 × (− 3) + 3 × 7 2 + 3 ⇒ y = − 6 + 21 5 ⇒ y = 155 ⇒ y = 3

The coordinates of the required point are (1,3).
Therefore, the correct option is 3.

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