## 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).

### Solution

5 : 7

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

⇒ 9*y* – 72 = 10*x* – 60

or 10*x* – 9*y* + 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).

#### SIMILAR QUESTIONS

Find the equation to the straight line cutting off an intercept of 5 units on negative direction of y-axis and being equally inclined to the axes.

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Find the equation of the right bisector of the line joining (1, 1) and (3, 5).

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Find the equations of the medians of a triangle, the coordinates of whose vertices are (–1, 6), (–3, –9) and (5, –8).

Find the equation of the line through (2, 3) so that the segment of the line intercepted between the axes is bisected at this point.