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प्रश्न
Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.
उत्तर
The end points of AB are A(-1, 7) and B (4, -3)
Therefore `(x_1 = -1, y_1 = 7) and (x_2 = 4, y_2 = -3 )`
Also , m = 2 and n = 3
Let the required point be P (x, y).
By section formula, we get
`x= (("m"x_2 + "n"x_1))/(("m"+"n")) , "y" = (("my"_2+"ny"_1))/(("m"+"n"))`
`⇒ x = ({ 2 xx 4 +3 xx (-1) })/(2+3) , "y"= ({2 xx (-3) + 3 xx 7})/(2+3)`
`⇒ x = (8-3) /5, "y" = (-6+21)/5`
`⇒ x = 5/5, "y" = 15/5`
Therefore, x = 1 and y = 3
Hence, the coordinates of the required point are (1, 3).
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Activity:
∴ By section formula,
∴ x = `("m"x_2 + "n"x_1)/square`,
∴ x = `(3 xx 8 + 1 xx 4)/(3 + 1)`,
= `(square + 4)/4`,
∴ x = `square`,
∴ y = `square/("m" + "n")`
∴ y = `(3 xx 5 + 1 xx (-3))/(3 + 1)`
= `(square - 3)/4`
∴ y = `square`
