In what ratio, the line joining (−1,1) and (5,7) is devided by the line x+y=4?
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Solution
Simplification of given data
Let line AB is the line joining the points A(−1,1)&B(5,7) and let line CD be x+y=4
Let line AB be divided by the line CD at point P.
Let k:1 be the ratio line AB is divided by the line CD.
If a point divides any line joining (x1,y1) & (x2,y2) in the ratio of m1:m2 then co-ordinate of that point are (m2x1+m1x2m1+m2,m2y1+m1y2m1+m2)
Point P which divide the line A(−1,1) & B(5,7) in k:1 ratio is P=((5)(k)+(−1)(1)k+1,(7)(k)+(1)(1)k+1)=(5k−1k+1,7k+1k+1)
Required point
Now point P(5k−1k+1,7k+1k+1) lies on the line CD
So, it will satisfy the equation of line CD
So, putting x=5k−1k+1,y=7k+1k+1 in x+y=4,