Question

Question 14 In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

Class X1 - Maths -Straight Lines Page 234

Answer 1

see attachment,
Let the point P divides the line joining the points A( -1, 1) and B(5, 7) in the ratio K:1

use section formula,
Then,
P = { (mx2 + nx1)/(m + n), (my2 + ny1)/(m+n)}
= { (k × 5 + 1 × -1)/(k+1), (k × 7 + 1 × 1 )/(k+1)}
= { (5k - 1)/(k + 1), (7k + 1)/(k + 1) }

point P will satisfy the line, x + y = 4
e.g ( 5k - 1)/(k + 1) + (7k + 1)/(k + 1) = 4
(5k - 1) + (7k + 1) = 4(k + 1)
12k = 4k + 4
8k = 4
k =1/2

hence, required ratio. is K:1 = 1 : 2 ( internally because ratio is positive)