Q. 524.6( 5 Votes )
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.
Answer :
Here, given points are A (12,5) and B (4, -3) and let the point dividing the line joining two points be P(x,2)
Let the ratio be m:n
By section formula,
x = 
, y = 
For point P(x,2),
x = 
…(1)
And 2 = 
…(2)
Solving 2 for finding ratio between m and n,
2 = 
2(m + n) = -3m +5n
2m + 2n = -3m +5n
∴ 5m = 3n
∴ 
= 
∴ m : n = 3 : 5
Now solving for equation 1, where m = 3 and n =5
x = 
∴ x = 
∴ x = 9
Hence, our point is (9, 2)
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