find the ratio in which the line 2x + 3y - 5 = 0 divideds the line segment joining the points (8,-9) and (2,1) . also find the coordinates of the point of division.

Let the co-ordinates be P (x, y). Let the ratio be m : n in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1)

 

Since this point P lies on the line joining the points (8, –9) and (2, 1) and divide the line segment in the  ratio m : n.

 

 

So, the co-ordinates of point P are

 

 

Since this point P also lies on the given line 2x + 3y – 5 = 0, so it must satisfy the equation of this line. so,

 

 

Hence m : n = 8: 1

 

and so the co-ordinates of point of division are

 

 

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