If a point P(2,1)   is located on the line segment connecting two points A(4,2)   and B(8,4),   then from the following choices, find the correct one.

# If a point   is located on the line segment connecting two points   and   then from the following choices, find the correct one.

1. A

2. B

3. C

4. D

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### Solution:

Given that, the points are A(4, 2) and B(8, 4) and   is located on the line segment.
Using the section formula, if a point (  ) divides the line joining the points (  ) and (${x}_{2},{y}_{2}\right)$ in the ratio   , then
.
Let    divides    in the ratio   .
Hence, m = k, n = 1.
Here,

Substitute the values in the formula, we get,
Comparing the x-coordinate,

As    is negative,   divides    in the ratio    externally.

Therefore, the condition is  .
Hence, option 1) is correct.

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