68. In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

68. The given eqn of line isl1: x + y = 4Let R divides the line joining two points P (?1,1) and Q (5,7) in ratio k:1. Then, Co-ordinate of R = (5k-1k+1, 7k+1k+1)As l1 divides line joining PQ, then R lies on l1i e, 5k-1k+1, 7k+1k+1=45k ?1 + 7k + 1= 4 (k + 1)12k = 4k + 48k = 4k = 12The ratio in which x + y = 4 divides line joining (?1,1) ad (5,7) is 12 :1 i.e., 1: 2.

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Ncert Solutions Maths class 11th Maths Class 11th Straight Lines

68. In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

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alok kumar singh | Contributor-Level 10

4 months ago

68. The given eqⁿ of line is

l1: x + y = 4

Let R divides the line joining two points P (?1,1) and Q (5,7) in ratio k:1. Then,

Co-ordinate of R = ( $(\frac{5 k - 1}{k + 1}, \frac{7 k + 1}{k + 1})$ )

As l₁ divides line joining PQ, then R lies on l₁

i e, $(\frac{5 k - 1}{k + 1}, \frac{7 k + 1}{k + 1})$ =4

5k ?1 + 7k + 1= 4 (k + 1)

12k = 4k + 4

8k = 4

k = $\frac{1}{2}$

The ratio in which x + y = 4 divides line joining (?1,1) ad (5,7) is $\frac{1}{2}$ :1 i.e., 1: 2.

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Kindly consider the following figure

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According to question,

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