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Question
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
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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 + 2))","((my_2 + ny_1)/(m + n)))`
Here it is said that the point `(-5, -21/5)` divides the points (-3,-1) and (-8,-9).
Substituting these values in the above formula we have,
`(-5, -21/5) = (((m(-8) + n(-3))/(m + n))","((m(-9) + n(-1))/(m+ n)))`
Equating the individual components we have,
`-5 = (m(-8) + n(-3))/(m + n)`
-5m - 5n = -8m - 3n
3m = 2n
`m/n = 2/3`
Therefore the ratio in which the line is divided is 2:3
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