Find the ratio in which the line segment joining the points A(3,8) and B(-9, 3) is divided by the Y- axis.

Find the ratio in which the line segment joining the points A(3,8) and B(-9, 3) is divided by the Y- axis.

Answer:-

Let the ratio in which the line AB is divided by the y-axis be k : 1.
The point on the y – axis be (0, y).

[left( 0, y right) = left( frac{k times left( – 9 right) + 1 times 3}{k + 1}, frac{k times 3 + 1 times 8}{k + 1} right)]

[ Rightarrow left( 0, y right) = left( frac{- 9k + 3}{k + 1}, frac{3k + 8}{k + 1} right)]

[ Rightarrow 0 = frac{- 9k + 3}{k + 1} ]

[ Rightarrow – 9k + 3 = 0]

[ Rightarrow k = frac{1}{3}]

Thus, the ratio is 1 : 3.

Chapter 5. Co-ordinate Geometry – Problem set 5 (Page 122)