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Question
If the point P (6, 7) divides the segment joining A(8, 9) and B(1, 2) in some ratio, find that ratio
Solution:
Point P divides segment AB in the ratio m: n.
A(8, 9) = (x1, y1), B(1, 2 ) = (x2, y2) and P(6, 7) = (x, y)
Using Section formula of internal division,
∴ 7 = `("m"(square) - "n"(9))/("m" + "n")`
∴ 7m + 7n = `square` + 9n
∴ 7m – `square` = 9n – `square`
∴ `square` = 2n
∴ `"m"/"n" = square`
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Solution
Point P divides segment AB in the ratio m : n.
A(8, 9) = (x1, y1), B(1, 2 ) = (x2, y2) and P(6, 7) = (x, y)
Using Section formula of internal division,
y = `("m"y_2 + "n"y_1)/("m" + "n")`
∴ 7 = `("m"(2) - "n"(9))/("m" + "n")`
∴ 7m + 7n = 2m + 9n
∴ 7m – 2m = 9n – 7n
∴ 5m = 2n
∴ `"m"/"n"` = `bb(2/5)`
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