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Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.

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#### Solution

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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