Question

Find the ratio in which y-axis divides the line segment joining the point (6,-4) and (-2,-7) Also find the point of intersection

Answer 1

Answer:

ratio of division of line segment = 3 / 1 & point of intersection is (0,-$\frac{25}{4}$)

Step-by-step explanation:

The points A(6,-4) & B(-2,-7) join to form a line segment.

Let y-axis divide the line in the ratio k / 1 .

On y-axis a point is in the form of (0,y)

⇒ 0 = -2k + 6 / k + 1 -----> (1)       &        y = -7k - 4 / k+ 1 -------> (2)

On solving (1) we get ,

⇒ 6 - 2k = 0

⇒ 2k = 6

⇒ k = 3 --------> (3)

∴ ratio of division = k / 1 = 3 / 1

On sub. (3) in (2) we get ,

⇒ y = -7(3) - 4 / 3 + 1

⇒ y = -21 - 4 / 4

⇒ y = -25 / 4

∴ The point of intersection is = (0,y) = (0,$\frac{-25}{4}$)