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.(CBSE 2014)
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
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.