Find the ratio in which the point P(x,2) divides the line segment joining the points A(12,5) and B(4,-3) . Also , find the value of x.
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Rahul Aryan
Rahul Aryan
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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.
Putting K = 3/5 in P , we get
X = ( 4 × 3/5 + 12 / ( 3/5 + 1 ) = 72/8 = 9.
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.
Putting K = 3/5 in P , we get
X = ( 4 × 3/5 + 12 / ( 3/5 + 1 ) = 72/8 = 9.
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