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प्रश्न
Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k.
उत्तर
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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