Question

2. The line x+y=4 divides the line joining the points (-1, 1)and (5,7) in the ratio ​

Answer 1

Answer:

2

Step-by-step explanation:

Option (2) 1:2 internally

Given points (1, -1) and (5, 7)

The equation of line joining these two points = (y-1)/(7-1) = (x+1)/(5+1)

y-1= x+1

Therefore, x-y+2 = 0 …(1)

Equation of the given line = x+y = 4

X+y-4 = 0 …(2)

On solving (1) and (2), the point of intersection (x, y) = (1, 3)

Let the point (1, 3) divide the line joining (-1, 1) and (5, 7) in the ratio of 1:k internally.

Now by using section formula, we get

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

2k= 4

k= 2

Hence, the line x + y = 4 divides the line joining the points (-1, 1) and (5, 7) in the ratio of 1:2 internally.