If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.

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#### Solution

The coordinates of the point dividing two points `(x_1,y_1)` and `(x_2,y_2)` in the ratio m:n is given as,

`(x,y) = (((lambdax_2 + x_1)/(lambda + 1))","((lambday_2 + y_1)/(lambda + 1)))` Where `lambda = m/n`

Here the two given points are *A*(1*,*4) and *B*(5*,*2). Let point *P*(*x, y*) divide the line joining ‘*AB*’ in the ratio 3:4

Substituting these values in the earlier mentioned formula we have,

`(x,y) = (((3/4(5) + (1))/(3/4 + 1))",((3/4(2) + (4))/(3/4 + 1)))`

`(x,y) = ((((15 + 4(1))/4)/((3 + 4)/4))","(((6 + 4(4))/4)/((3+4)/4)))`

`(x,y) = ((19/7)","(22/7))`

Thus the co-ordinates of the point which divides the given points in the required ratio are `(19/7 , 22/7)`

Concept: Coordinate Geometry

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