The ratio in which (2,3) divides the line segment joining $(4, 8), (- 2, - 7)$ is

2 : 1

externally

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2 : 3

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4 : 3

externally

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1 : 2

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Solution

The correct option is A $2 : 1$ externally
Given, $A (4, 8), B (- 2, - 7)$ and $(2, 3)$ let this divdes line AB in m:n ratio
we know, $(2, 3) = (\frac{m (- 2) + n (4)}{m + n}, \frac{m (- 7) + n (8)}{m + n})$
Now by comparing co-ordinates we get,
$2 = \frac{- 2 m + 4 n}{m + n}$
$\Rightarrow 2 m + 2 n = - 2 m + 4 n$
$\Rightarrow 4 m = 2 n$
$\frac{m}{n} = \frac{2}{4} = \frac{1}{2}$

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Similar questions

(- 2, 4), (2, 7)

2 : 1

P (2, 3)

A (- 2, - 7)

B (4, 8)

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 $(\frac{9}{5}, \frac{2}{5}, \frac{- 1}{5})$ .

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