Question

In what ratio does the line segment joining points (-1,1) and (5,7) divides the line of x+y=4

Answer 1

Answer:

Step-by-step explanation:

CBSE XI >> Math >> Straight Lines

Next similar questionQ)

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

(A)2:1(C)1:3(B)1:2(D)3:1(A)2:1(B)1:2(C)1:3(D)3:1

A)

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Equation of a line joining two points (x1,y1)(x1,y1) and (x2,y2)(x2,y2) is y−y1y2−y1y−y1y2−y1=x−x1x2−x1=x−x1x2−x1

Section formula : mx2+nx1m+nmx2+nx1m+n,my2+ny1m+n,my2+ny1m+n

The given points are (-1, 1) and (5,7).

Hence equation of the line joining the above points is

y−17−1y−17−1=x−(−1)5−(−1)=x−(−1)5−(−1)

⇒y−16⇒y−16=x+16=x+16

⇒y−1=x+1⇒y−1=x+1

or x−y+2=0x−y+2=0---------(1)

Equation of the given line is

x+y−4=0x+y−4=0---------(2)

The point of intersection of the lines (1) and (2) is

x−y=−2x−y=−2

x+y=4x+y=4

2x=22x=2

⇒x=1⇒x=1 and y=3y=3

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

By applying the section formula,

1=k(−1)+1(5)k+11=k(−1)+1(5)k+1

⇒k+1=−k+5⇒k+1=−k+5

⇒2k=4⇒2k=4

or k=2k=2

Hence the line joining the points (-1, 1) and (5,7) is divided by line

x+y=4x+y=4 in the ratio 1 : 2

Answer 2

the ratio is 1:2....