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Question
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Solution
The co-ordinates of a point which divided two points `(x_1,y_1)` and `(x_2, x_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 it is said that the point (−4,6) divides the points A(−6,10) and B(3,−8). Substituting these values in the above formula we have,
`(-4, 6) = (((m(3) + n(-6))/(m + n))"," ((m(-8) + n(10))/
(m + n)))`
Equating the individual components we have,
`-4 = (m(3) + n(-6))/(m + n)`
-4m - 4n = 3m - 6n
7m = 2n
`m/n = 2/7`
Therefore the ratio in which the line is divided is 2 : 7
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