Assertion (A): The coordinates of a point which divides a line segment joining the points (-3, 4) and (7, -6) in the ratio 1 : 2 internally are $\Big(\dfrac{1}{3}, \dfrac{2}{3}\Big)$.

Reason (R): The coordinates of the point which divides the line segment joining the points (x₁, y₁) and (x₂, y₂) internally in the ratio m : n are given by $\Big(\dfrac{mx$2 + nx1}{m + n}, \dfrac{my2 + ny1}{m + n}\Big).

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Let point P be (x, y), which divides line segment joining the points (-3, 4) and (7, -6) in the ratio 1 : 2.

Given,

m₁ : m₂ = 1 : 2

By section-formula,

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

Substitute values we get:

$\Rightarrow (x, y) = \Big(\dfrac{1(7) + 2(-3)}{1 + 2}, \dfrac{1(-6) + 2(4)}{1 + 2}\Big) \\[1em] = \Big(\dfrac{7 - 6}{3}, \dfrac{-6 + 8}{3}\Big) \\[1em] = \Big(\dfrac{1}{3}, \dfrac{2}{3}\Big).$

So, Assertion is true.

The coordinates of the point which divides the line segment joining the points (x₁, y₁) and (x₂, y₂) internally in the ratio m : n are given by $\Big(\dfrac{mx$2 + nx1}{m + n}, \dfrac{my2 + ny1}{m + n}\Big).

So, reason is true.

Both A and R are true.

Hence, Option 3 is the correct option.