Assertion (A): PQR is an equilateral triangle. The co-ordinates of point Q are (0, $2\sqrt{2}$).

Reason (R): In ΔOPQ,

OQ² = PQ² - OP² = 4² - 2² = 12.

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.

The coordinates of R(0, 2) and P(0, -2).

Using distance formula,

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

PR = $\sqrt{(0 - 0)^2 + (-2 - 2)^2} = \sqrt{(-4)^2} = \sqrt{16} = 4$ units.

Given equilateral triangle PQR.

∴ PQ = QR = PR = 4 units.

In an equilateral triangle, a perpendicular drawn from one of the vertices to the opposite side bisects the side.

∴ OP = $\dfrac{1}{2}$ x PR = ​$\dfrac{1}{2}$ x 4 = 2 units.

In right angle triangle OPQ,

By pythagoras theorem,

⇒ QP² = OP² + OQ²

⇒ OQ² = QP² - OP²

⇒ OQ² = 4² - 2²

⇒ OQ² = 16 - 4

⇒ OQ² = 12

⇒ OQ = $\sqrt{12}$

⇒ OQ = $2\sqrt{3}$

Since, OQ = $2\sqrt{3}$ units and Q lies on x-axis.

Co-ordinates of Q = ($2\sqrt{3}$, 0).

∴ A is false, but R is true.

Hence, option 2 is the correct option.