find the ratio in which the point (X, 2) divides the line segment joining the points of A(12,5) and B(4,-3).also find the value of X.
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Answered by
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Since P divides the line segment joining points A(12,5) and B(4,-3) therefore,
x= \frac{m x_{2}+n x_{1} }{m+n}x=m+nmx2+nx1 and
y= \frac{m y_{2}+n y_{1} }{m+n}y=m+nmy2+ny1
where m:n is the ratio;
(x₁,y₁)=(12,5) and (x₂,y₂)=(4,-3) and (x,y)=(x,2) (coordinate of P)
∴, 2= \frac{-3m+5n}{m+n}2=m+n−3m+5n
or, 2m+2n=-3m+5n2m+2n=−3m+5n
or, 2m+3m=5n-2n2m+3m=5n−2n
or, 5m=3n5m=3n
or, \frac{m}{n}= \frac{3}{5}nm=53
∴, x= \frac{3.4+5.12}{3+5}x=3+53.4+5.12
or, x= \frac{12+60}{8}x=812+60
or, x=72/8x=72/8
or, x=9x=9
∴, The required ratio is \frac{3}{5}53 and x=9x=9 . Ans.
x= \frac{m x_{2}+n x_{1} }{m+n}x=m+nmx2+nx1 and
y= \frac{m y_{2}+n y_{1} }{m+n}y=m+nmy2+ny1
where m:n is the ratio;
(x₁,y₁)=(12,5) and (x₂,y₂)=(4,-3) and (x,y)=(x,2) (coordinate of P)
∴, 2= \frac{-3m+5n}{m+n}2=m+n−3m+5n
or, 2m+2n=-3m+5n2m+2n=−3m+5n
or, 2m+3m=5n-2n2m+3m=5n−2n
or, 5m=3n5m=3n
or, \frac{m}{n}= \frac{3}{5}nm=53
∴, x= \frac{3.4+5.12}{3+5}x=3+53.4+5.12
or, x= \frac{12+60}{8}x=812+60
or, x=72/8x=72/8
or, x=9x=9
∴, The required ratio is \frac{3}{5}53 and x=9x=9 . Ans.
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Answer:
Let the required ratio be K:1.
Then, By section formula,the Coordinates of P are :
P ( 4K + 12/K + 1 , -3K + 5 / K + 1 )
But , this points is given as P ( x , 2).
Therefore,
⇒ -3K + 5 / K + 1 = 2
⇒ -3K + 5 = 2K + 2
⇒ 5K = 3
⇒ K = 3/5.
So, the required ratio is 3:5.
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