Assertion (A): The distance between the points A(x, 2x) and B(x, 0) is 4 unit, the point B is (2, 0).

Reason (R): $\sqrt{(x - x)^2 + (2x - 0)^2}$ = 2

⇒ x² = 4 and x = ± 2

1. A is true, but R is false.

2. A is false, but R is true.

3. Both A and R are true, and R is the correct reason for A.

4. Both A and R are true, and R is the incorrect reason for A.

Given, the distance between the points A(x, 2x) and B(x, 0) is 4 unit.

By distance formula,

Distance between two points = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

Substituting the values, we get :

$\Rightarrow 4 = \sqrt{(x - x)^2 + (2x - 0)^2}\\[1em] \Rightarrow 4 = \sqrt{0^2 + (2x)^2}\\[1em] \Rightarrow 4 = \sqrt{4x^2}\\[1em] \Rightarrow 4^2 = 4x^2\\[1em] \Rightarrow 16 = 4x^2\\[1em] \Rightarrow x^2 = \dfrac{16}{4}\\[1em] \Rightarrow x^2 = 4\\[1em] \Rightarrow x = \sqrt{4}\\[1em] \Rightarrow x = \pm 2.$

The coordinates of B = (x, 0) = (2, 0) or (-2, 0)

∴ A is false, but R is true.

Hence, option 2 is the correct option.