Question

Assertion: The endpoints of a diameter of a circle are (3, −5) and (1, 1). Its centre will be (2, −2).

Reason: The coordinates of the mid-point of line segment joining (x₁, y₁) and (x₂, y₂) are `((x_1 + x_2)/2, (y_1 + y_2)/2)`.

Options

• Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

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

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Explanation:

The centre equals the midpoint:

= `((3 + 1)/2, (−5 + 1)/2)`

= (2, −2)

Using the midpoint formula `(x_1 + x_2)/2, (y_1 + y_2)/2` for endpoints of a diameter gives the circle’s centre.