Question

Point A (3, 4) is the centre of a circle. If one of its diameters has one end as (7, 8); the other end of this diameter is ______.

Options

• (1, 0)

• (0, 1)

• (−1, 0)

• (0, −1)

Answer 1

Point A (3, 4) is the centre of a circle. If one of its diameters has one end as (7, 8); the other end of this diameter is (−1, 0).

Explanation:

Given,

A(3, 4) is center and let B(7, 8) be one end of the diameter.

Let other end of diameter be C(x, y).

By mid-point formula,

Mid-point = `((x_1+x_2)/2, (y_1+y_2)/2)`

From figure,

A is the mid-point of BC.

∴ (3, 4) = `((x + 7)/2​,(y + 8)/2)`

⇒ `(x + 7)/2 = 3 and (y + 8)/2 = 4`

⇒ x + 7 = 6 and y + 8 = 8

⇒ x = 6 − 7 and y = 8 − 8

⇒ x = −1 and y = 0

∴ C = (−1, 0).