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Question
Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.
Solution
Let P divides AB in a ratio of λ : 1
Therefore, coordinates of the point P are `((6lambda+2)/(lambda + 1), (-3lambda + 3)/(lambda + 1))`
Given that coordinates of the point P are (4, m).
`=> (6lambda + 2)/(lambda + 1) = 4`
`=> 6lambda + 2 = 4lambda + 4`
`=> lambda = 1`
Hence, the point P divides AB in a ratio of 1 : 1.
Replacing the value of λ = 1 in y-coordinate of P, we get
`(-3(1)+3)/(1+1) = m`
`=> m = 0`
Thus, y-coordinate of P is equal to 0.
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