Point P   divides the line segment joining the points A(2,1)   and B(5,−8)   such that AP AB = 1 3 .   If P   lies on the line 2x−y+k=0  , then the value of k   from the following choices is:

# Point   divides the line segment joining the points   and   such that   If   lies on the line  , then the value of   from the following choices is:

1. A
-2
2. B
-4
3. C
-6
4. D
-8

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### Solution:

Given that, the points are A(2, 1) and B(5, -8) and
lies on the line  .
If P(x, y) divides the line segment with the coordinates   in the ratio m:n internally, then the section formula is given by,

We have to find the ratio for AP:PB.
So,  .
Here, m = 1, n = 2.

By using section formula, the coordinate of x is given by,
By using section formula, the coordinate of y is given by,

Substitute the value   in the line equation, we get,

The value of k is -8.
Hence, option 4) is correct.

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