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