If M(9p−2,−q)   divides the line segment joining L(3p+1,−3)   and N(8p,5)   in the ratio 3:1  , find the values of p   and q  .

# If   divides the line segment joining   and   in the ratio  , find the values of   and  .

1. A
and
2. B
and
3. C
and
4. D
and

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### Solution:

Given that,   divides the line segment joining   and  .
The ratio is  .
If P(x, y) divides the line segment with the coordinates   in the ratio m:n internally, then the section formula is given by,
.
Here, m = 3, n = 1.
.
Substituting the values in the formula, we get,

Equating the x-coordinates, we get,

Equating the y-coordinates, we get,
So, the coordinates is  .
The value of    and  .
Hence, option 4) is correct.

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