Question

determine the ratio in which the line x-y-2=0 dives the linesegment joining (3,-1) and (8,9)
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i need the perfect process

Answer 1

Let the points diveides the line in the ratio k:1
x,y=8k+3/k+1,9k-1/k+1
x,=8k+3/k+1,y=9k-1/k+1
x-y-2=0
8k+3/k+1 -9k-1/k+1 =2
-k+4/k+1=2
-k+4=2k+3
3k=2
k=2/3
Hence,the line divides the points in the ratio 2:3

Answer 2

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

The coordinates of the point = (8k + 3/k + 1, 9k - 1/k + 1)

Given that the point lies on line x - y - 2 = 0.

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

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

8k + 3 - 9k + 1 - 2k - 2 = 0

8k - 9k - 2k + 1 - 2 = -3

-3k - 1 = -3

-3k = -2

k = 2/3.


Hence the line divides the line segment joining A(3,-1) and (8,9) in the ratio 2:3.


Hope this helps!