Assertion (A): The point P(3, -1) divides the line segment joining the points A(1, -3) and B(6, 2) internally in the ratio 2 : 3.

Reason (R): The coordinates of the point which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁ : m₂ are $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big).

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

By section-formula,

The coordinates of the point which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁ : m₂ are

$\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big).

So, reason (R) is true.

Let us find the point P which divides the line segment joining A(1, -3) and B(6, 2) in the ratio 2 : 3, by section-formula.

$\Rightarrow \text{P} = \Big(\dfrac{2 \times 6 + 3 \times 1}{2 + 3}, \dfrac{2 \times 2 + 3 \times (-3)}{2 + 3}\Big)\\[1em] = \Big(\dfrac{12 + 3}{5}, \dfrac{4 - 9}{5}\Big)\\[1em] = \Big(\dfrac{15}{5}, \dfrac{-5}{5}\Big)\\[1em] = (3, -1)$

So, assertion (A) is true.

Thus, both A and R are correct, and R clearly explains A.

Hence, option 3 is the correct option.