Question

Assertion (A): PQR is an equilateral triangle. The co-ordinates of point Q are (0, `2sqrt2`).

Reason (R): In ΔOPQ, OQ² = PQ² − OP² = 4² − 2² = 12.

Options

• A is true, R is false.

• A is false, R is true.

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

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

Answer 1

A is false, R is true.

Explanation:

• Reason (R) is true because in the right-angled triangle OPQ, the side length PQ = 4 (since PQR is an equilateral triangle with side PR = 4 units from −2 to 2 on the y-axis) and OP = 2. Applying the Pythagorean theorem gives OQ² = PQ² − OP² = 4² − 2² = 12.
• Assertion (A) is false because the coordinates of point Q derived from OQ = `sqrt12 = 2sqrt3  "are" (2sqrt3, 0)` since it lies on the x-axis, whereas Assertion (A) incorrectly states the coordinates are (0,`2sqrt2`​).