Find The Ratio In Which The Line Segment Joining The Points (2, 3) And (4, 5) Is Divided By The Line Joining (6, 8) And (–3, –2).

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Question

Find the ratio in which the line segment joining the points (2, 3) and (4, 5) is divided by the line joining (6, 8) and (–3, –2).

5 : 7
2 : 3
3 : 4
7 : 9

diffcult

Solution

Correct option is

5 : 7

The equation of the line passing through (6, 8) and (–3, –2) is

⇒ 9y – 72 = 10x – 60

or 10x – 9y + 12 = 0 … (i)

Let the required ratio be λ : 1.

Now the coordinates of the point P which divides the line segment joining the points (2, 3) and (4, 5) in the ratio λ : 1 is

Clearly P lies on (i), then

∴ The required ratio,

= –5 : 7

Hence the required ratio is 5 : 7 (externally).

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