Find the ratio in which the point 2 y


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FIND THE RATIO IN WHICH THE POINT (2,y) DIVIDES THE LINE SEGMENT JOINING THE POINTS A(-2,2) & B(3,7) . ALSO FIND THE VALUE OF ' y' ?

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Let Q(2,y) divides the line segment AB in m:n ratio.
∴, x=(mx₂+nx₁)/(m+n)
Here, (x₁,y₁)=(-2,2) , (x₂,y₂)=(3,7)  and (x,y)=(2,y)
2={3m+(-2n)}/(m+n)
or, 2m+2n=3m-2n
or, 2m-3m=-2n-2n
or, -m=-4n
or, m/n=4/1
∴, m:n=4:1
∴, y=(my₂+ny₁)/(m+n)
or, y=(4.7+1.2)/(4+1)
or, y=(28+2)/5
or, y=30/5
or, y=6
∴, the required ratio is 4:1 and y=6. Ans.

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