In what ratio, the line joining (- 1, 1) and (5, 7) is divisible by the line x + y = 4 ?

Solution:

The equation of the line joining the points (- 1, 1)and (5, 7) is given by

y - 1 = [(7 - 1)/(5 + 1)]( x + 1)

y - 1 = 6/6 ( x + 1)

x - y + 2 = 0 ....(1)

The equation of the given line is

x + y = 4 ....(2)

The points of intersection of line (1) and (2) is given by x = 1 and y = 3

Let point (1, 3) divides the line segment joining (- 1, 1) and (5, 7) in the ratio 1 : k.

Accordingly, by section formula

(1, 3) = {[k(- 1) + 1(5)]/(1 + k), [k(1) + 1(7)]/(1 + k)}

⇒ (1, 3) = [(- k + 5)/(1 + k), (k + 7)/(1 + k)]

⇒ (- k + 5)/(1 + k) = 1, (k + 7)/(1 + k) = 3

Therefore,

(- k + 5)/(1 + k) = 1

⇒ - k + 5 = 1 + k

⇒ 2k = 4

⇒ k = 2

Thus, the line joining the points (- 1, 1) and (5, 7) is divisible by the line x + y = 4 in the ratio 1 : 2

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NCERT Solutions Class 11 Maths Chapter 10 Exercise ME Question 14

In what ratio, the joining (- 1, 1)and (5, 7) is divisible by the line x + y = 4 ?

Summary:

The line joining (- 1, 1) and (5, 7) is divisible by the line x + y = 4 in the ratio 1 : 2