# In What Ratio Does the Line X -y-2=0 Divide the Line Segment Joining the Points A(3,1) and B (8,9) ? - Mathematics

In what ratio does the line x -y-2=0  divide the line segment joining the points A(3,1) and B (8,9) ?

#### Solution

Let the line x-y-2=0  divide the line segment joining the points A (3,1) and B (8,9)  in the ratio k : 1 at P.

Then, the coordinates of P are

p ((8k+3)/(k+1),(9k-1)/(k+1))

Since, P lies on the line  x - y -2 =0 we have:

 ((8k+3)/(k+1)) - ((9k-1)/(k+1)) -2=0

⇒ 8k + 3- 9k + 1- 2k - 2 = 0

⇒ 8k -9k -2k +3+1 - 2 = 0

⇒ -3k +2 = 0

⇒ - 3k=-2

⇒ k =2/3

So, the required ratio is  2/3:1 which is equal to 2 : 3.

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 19