Find the ratio in which the point Q( -3 , P ) divides the line segment AB joining the points A( -5 , -4 ) and B( -2 , 3 ) . Also find the value of P.
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Let Q(-3,P) divides the line segment AB in m:n ratio.
∴, x=(mx₂+nx₁)/(m+n)
Here, (x₁,y₁)=(-5,-4) , (x₂,y₂)=(-2,3) and (x,y)=(-3,P)
-3={-2m+(-5n)}/(m+n)
or, -3m-3n=-2m-5n
or, -3m+2m=-5n+3n
or, -m=-2n
or, m/n=2/1
∴, m:n=2:1
∴, P=(my₂+ny₁)/(m+n)
or, P={2×3+(1×-4)}/(2+1)
or, P=(6-4)/3
or, P=2/3
∴, p=2/3 and m:n=2:1 Ans.
∴, x=(mx₂+nx₁)/(m+n)
Here, (x₁,y₁)=(-5,-4) , (x₂,y₂)=(-2,3) and (x,y)=(-3,P)
-3={-2m+(-5n)}/(m+n)
or, -3m-3n=-2m-5n
or, -3m+2m=-5n+3n
or, -m=-2n
or, m/n=2/1
∴, m:n=2:1
∴, P=(my₂+ny₁)/(m+n)
or, P={2×3+(1×-4)}/(2+1)
or, P=(6-4)/3
or, P=2/3
∴, p=2/3 and m:n=2:1 Ans.
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5
Answer:
m:n=2:1 Ans.
Step-by-step explanation:
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