Question

EXERCISE 7.4 (Optional)
1. Determine the ratio in which the line 2x + y-4-0 divides the line segment joining the
points A(2, 2) and B(3,7).
​

Answer 1

Answer:

10th

Maths

Coordinate Geometry

Section Formula

Determine the ratio in whic...

MATHS

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Asked on December 26, 2019 by

Sanyog Sadique

Determine the ratio in which the line 2x + y -4 = 0 divides the line segment joining A(2, -2) and B(3, 7)

MEDIUM

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ANSWER

Using the section formula, if a

point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n, then (x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let the ratio be k:1

Substituting (x

1

,y

1

)=(2,−2) and (x

2

,y

2

)=(3,7) in the

section formula, we get (

k+1

k(3)+1(2)

,

k+1

k(7)+1(−2)

)=(

k+1

3k+2

,

k+1

7k−2

)

Since 2x+y−4=0 divides the line at P, this point will lie on the

2(

k+1

3k+2

)+

k+1

7k−2

−4=0

6k+4+7k−2−4k−4=0

9k=2

k=

9

2

Hence, the ratio is 2:9