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Question
In what ratio does the point `(24/11, y)` divide the line segment joining the points P(2, –2) and Q(3, 7)? Also find the value of y.
Solution
Let the point P`(24/11, y)` divide the line PQ in the ratio k : 1.
Then, by the section formula:
`x = (mx_2+nx_1)/(m+n), y = (my_2 + ny_1)/(m + n)`
The coordinates of R are `(24/11, y)`
`24/11 = (3k + 2)/(k + 1), y = (7k - 2)/(k + 1)`
`=>24(k + 1) = 33k + 22, y(k + 1)= 7k - 2`
⇒24k + 24 = 33k + 22 , yk + y =7k − 2
⇒2 = 9k
`=> k = 2/9`
Now consider the equation yk + y = 7k - 2 and put `k = 2/9`
`=> 2/9y + y = 14/9 - 2`
`=> 11/9y = (-4)/9`
`=> y = (-4)/11`
Therefore, the point R divides the line PQ in the ratio 2 : 9
And, the coordinates of R are `(24/11, (-4)/11)`
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Activity:
∴ By section formula,
∴ x = `("m"x_2 + "n"x_1)/square`,
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= `(square + 4)/4`,
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