Question

Assertion (A): The coordinates of one end of a diameter of a circle are (1, 4). If its centre is at (2, –3), then the coordinates of the other end of the diameter are (–3, –10).

Reason (R): Centre of a circle is equidistant from each end of a diameter.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is false, but R is true.

Explanation:

The centre of a circle is the midpoint of a diameter. If one endpoint is (1, 4) and centre is (2, –3), the other endpoint is $$(2 \cdot 2 - 1, 2(-3) - 4) = (3, -10)$$ not (–3, –10). Hence A is false; R is true.