A point $R (2, - 5)$ divides the line segment joining the point $A (- 3, 5)$ and $B (4, - 9)$ in the ratio of?

5 : 2

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5 : 1

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2 : 5

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3 : 2

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Solution

The correct option is A $5 : 2$
We have:
$A = (x_{1}, y_{1}) = (- 3, 5)$ and
$B = (x_{2}, y_{2}) = (4, - 9)$

Let us assume that $R (x, y) = (2, - 5)$ divides $A B$ in the ratio $m : n$ , then using section formula:
$x = \frac{m x_{2} + n x_{1}}{m + n}$
$2 = \frac{4 m + (- 3) n}{m + n}$

$2 m - 5 n = 0 \dots (1)$

And, $y = \frac{m y_{2} + n y_{1}}{m + n}$
$- 5 = \frac{- 9 m + 5 n}{m + n}$

$2 m - 5 n = 0 \dots (2)$

In both the cases, we have:
$2 m = 5 n$
$\frac{m}{n} = \frac{5}{2}$
$∴ m : n = 5 : 2$

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Similar questions

Which of the following statments are correct?

1. The coordinates of the point which divides the line segment joining the points

$(1, - 2, 3)$ and $(3, 4, - 5)$ internally in the ratio $2 : 3$ is $(- 3, - 14, 19)$ .

2. The coordinates of the point which divides the line segment joining the points

$(1, - 2, 3)$ and $(3, 4, - 5)$ externally in the ratio $2 : 3$ is $(\frac{9}{5}, \frac{2}{5}, \frac{- 1}{5})$ .

Ratio in which line $2 x + 3 y - 5 = 0$ divides the line segment joining the points A(8 , -9) and B(2 , 1) is .

2 x + y - z = 3

a = (2, 1, 3), b = (9, - 2, 5)

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