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प्रश्न
Find the ratio in which the point (2, y) divides the line segment joining the points A (-2,2) and B (3, 7). Also, find the value of y.
उत्तर
The co-ordinates of a point which divided two points`(x_1,y_1)` and `(x_2,y_2)` internally in the ratio m:n is given by the formula,
`(x,y) = ((mx_2 + nx_1)/(m + n)), ((my_2 + ny_1)/(m+n)))`
Here we are given that the point P(2,y) divides the line joining the points A(−2,2) and B(3,7) in some ratio.
Let us substitute these values in the earlier mentioned formula.
`(2,y) = (((m(3) +n(-2))/(m + n))"," ((m(7)+n(2))/(m+n)))`
Equating the individual components we have
`2 = (m(3) + n(-2))/(m + n)`
2m + 2n = 3m - 2n
m - 4n
`m/n = 4/1`
We see that the ratio in which the given point divides the line segment is 4: 1.
Let us now use this ratio to find out the value of ‘y’.
`(2,y) = (((m(3) + n(-2))/(m + n))"," ((m(7) + n(2))/(m + n)))`
`(2,y) = (((4(3) + 1(-2))/(4 +1))","((4(7) + 1(2))/(4 +1)))`
Equating the individual components we have
`y = (4(7) + 1()2)/(4 + 1)`
y = 6
Thus the value of ‘y’ is 6
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