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Question
Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k.
Solution
Let A(x1, y1), B(x2, y2) and P(x, y) be the given points.
Here, x1 = 8, y1 = 9, x2 = 1, y2 = 2, x = k, y = 7
∴ By section formula,
`y = (my_2 + ny_1)/(m + n)`
∴ `7 = (2m + 9n)/(m + n)`
∴ 7(m + n) = 2m + 9n
∴ 7m + 7n = 2m + 9n
∴ 5m = 2n
∴ `m/n = 2/5`
m : n = 2 : 5
`x = (mx_2 + nx_1)/(m + n)`
∴ `k = (2(1) + 5(8))/(2 + 5)`
∴ `k = (2 + 40)/(7)`
∴ `k = (42)/(7)`
∴ k = 6
∴ Point P divides seg AB in the ratio 2 : 5, and the value of k is 6.
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