Q15 of 184 Page 10

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

Let C(x, 2) divides the line segment AB in the ratio m:n

Here, (x, y) = (x, 2); (x₁, y₁) = (-3, -4) and (x₂, y₂) = (3, 5)

So,

⇒ 2m + 2n = 5m – 4n

⇒ 2m – 5m = -4n – 2n

⇒ -3m = -6n

⇒ m = 2n

Now, the ratio is 2:1

Now,

⇒ 3x = 6 – 3

⇒ 3x = 3

⇒ x = 1

Hence, the ratio is 2:1 and the division is internal and the value of x = 1

In what ratio does the point (-4,6) divide the line segment joining the point A(-6,10) and B (3,-8)?

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

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

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.