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Question

The line x+y=10 divides line segment AB in the ratio a:1. Find the value of a.


  1. 2

  2. 12

  3. 1

  4. 3


Solution

The correct option is C

1


The point, say P(x,y), divides the line AB into the ratio a:1. The equation for the point that divides a line in the ratio m : n is,
((n×x1+m×x2)m+n,n×y1+m×y2m+n)
Where (x1,y1) and (x2,y2) are the coordinates of the endpoints of the line segment.
Applying the formula, we get (1×2+a×6)a+1,1×4+a×8a+1)
This point lies on the line x+y=10, so substitute the points in the equation for the line.
(1×2+a×6)a+1+1×4+a×8a+1=106a+2+8a+4=10(a+1)4a=4a=1

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