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Question
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
Options
−2 : 3
−3 : 2
3 : 2
2 : 3
Solution
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 + n y_1)/(m + n ))`
Here it is said that the point (4, 5) divides the points A(2,3) and B(7,8). Substituting these values in the above formula we have,
`(4,5) = ((m(7)+n(2))/(m+n) , (m(8)+n(3))/(m+n))`
Equating the individual components we have,
`4 = ((m (7) + n(2) )/(m+n)) `
`4m + 4n = 7m + 2 n`
`3m = 2n `
`m/n = 2/3`
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