The mid-point P of the line segment joining the points A (- 10, 4) and B (- 2, 0) lies on the line segment joining the points C (- 9,-4) and D (- 4, y). Find the ratio in which P divides CD. Also, find the value of y.

Question

Philoid · Accepted Answer

Here given points are A (- 10, 4) and B (- 2, 0)and the points of other segment line are C (- 9,-4) and D (- 4, y)

Let the point of intersection between AB and CD be P

By midpoint formula.

x = , y =

For midpoint of AB,

e = , d = …(say)

e = -6 and d = 2 …(1)

By section formula,

x = , y =

For point P on CD, where ratio is m:n,

-6 = and 2 =

Solving for m and n,

-6 =

∴-6(m + n) = -4m -9n

6m + 6n = 4m + 9n

2m = 3n

∴ =

∴ Ratio is 3:2

Now solving for y, where m = 3 and n = 2,

2 =

∴ 3y -8 = 10

∴ 3y = 18

∴y = 6