Sum

In what ratio is the line joining A(0, 3) and B (4, -1) divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis

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#### Solution

Let the line segment AB intersects the x-axis by point P (x, 0) in the ratio k: 1.

`therefore (x,0)=((kxx4+1xx0)/(k+1),(kxx(-1)+1xx3)/(k+1))`

`therefore (x,0)=((4k)/(k+1),(-k+3)/(k+1))`

`=>0=(-k+3)/(k+1)`

`=>k=3`

Thus, the required ratio in which P divides AB is 3: 1.

Also, we have:

`x=(4k)/(k+1)`

`=>x=(4xx3)/(3+1)=12/4=3`

Thus, the co-ordinates of point P are (3, 0).

Concept: Section Formula

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