Question

Find the ratio in which line formed by joining (-1,1) and(5,7) is divided by the line x+y=4

Answer 1

let the ratio be k:1
now
coordinates of the point of intersection :
5k-1/k+1 , 7k+1/k+1
now
this point must satisfy the equation of the line
therefore
5k-1/k+1 + 7k+1/k+1 = 4
12k/k+1 = 4
12k = 4k+4
8k = 4
K = 4/8 = 1/2
therefore
the line divide it in the ratio 1:2

Answer 2

Given: line formed by joining (-1,1) and(5,7) is divided by the line x+y=4

To find: Find the ratio

Solution: To find the ratio in which the given line is dividing the line with points (-1,1) and(5,7)

we can write the line with the formula as

(y-y1)/(y2-y1)= (x-x1)/(x2-x1)

here (x1,y1), (x2,y2) will be the coordinates of two points connecting the line

on putting the values we will get the equation of line as

x-y+2=0

so the first equation will be x+y-4=0 and the second us x-y+2=0

on solving both the equation we will get its intersection point and that is (1,3)

Let say this intersection point divides the line x-y+2=0 in ratio 1:r

so according to the section formula, we can write it as

1 = ( k×-1 + 1×5 ) / ( k+1)

on solving we get k=2

Therefore, we can say that the ratio in which the line formed by joining (-1,1) and(5,7) is divided by the line x+y=4 is 1:2.