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Question

Determine the ratio in which the line 2x+y4=0 divides the line segment joining the points A(2, -2) and B (3, 7).
 


  1. 2 : 9

  2. 9 : 2

  3. 9 : 1

  4. 1 : 9


Solution

The correct option is A

2 : 9


Let the required ratio be k : 1 and let point C divide them in the above ratio.

We know that the coordinates of the point that divides a line segment in the ratio m : n is given by

(n×x1+m×x2m+n,n×y1+m×y2m+n)

where (x1,y1) and (x2,y2) are the coordinates of the endpoints of the line segment.

Coordinates of C are (3k+2k+1,7k2k+1)

Since point C lies on the line represented by the equation
2x+y4=0, it will satisfy the equation.

So we have

2(3k+2k+1)+(7k2k+1)4=0

2(3k+2)+(7k2)=4×(k+1)

6k+4+7k24k4=0

9k2=0

k=29

The required ratio is k : 1= 2 : 9.

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