Q16 of 184 Page 10

In what ratio does the x-axis divide the line segment joining the points (2,-3) and (5,6).

Let the line segment A(2, -3) and B(5, 6) is divided at point P(x,0) by x-axis in ratio m:n

Here, (x, y) = (x, 0); (x₁, y₁) = (2, -3) and (x₂, y₂) = (5, 6)

So,

⇒ 0 = 6m – 3n

⇒ -6m = -3n

Hence, the ratio is 1:2 and the division is internal.

Find the ratio in which the line segment joining (-3,10) and (6,-8) is divided by (-1,6)

Find the ratio in which the line segment joining (-3,-4) and (3,5) is divided by (x,2). Also, find x.

Find the ratio in which the line segment joining A(1,-5) and B(-4,5) is divided by the x-axis. Also, find the coordinates of the point of division.

Find the ratio in which the y-axis divides the line segment joining points (5,-6) and (-1,-4). Also, find the point of intersection.