Question

AB is a diameter of a circle with centre O, where A and B are (6, 2) and (4, -4) respectively. Then coordinates of O are _

Answer 1

• GIVEN:-

1. Coordinate of A (6,2)
2. Coordinate of B (4,-4)
3. AB is the diameter of cricle with centre O.

• To Find:-

Coordinates of O.

• SOLUTION:-

Let the coordinate of the centre of the circle be O(x, y).

It is said that AB is the diameter and O is the centre.

(refer to the attachment)

Therefore by applying Mid-Point Formula,

$\large\boxed{\sf{For\:x=\frac{x_1+x_2}{2}}}$

$\large\boxed{\sf{For\:y=\frac{y_1+y_2}{2}}}$

$\large{\sf{Let\:6\:and\:4\:be\:x_1\:and\:x_2\:respectively.}}$

and

$\large{\sf{Let\:2\:and\:-4\:be\:y_1\:and\:y_2\:respectively.}}$

By putting the values,

$\large\Longrightarrow{\sf x=\huge\frac{x_1+x_2}{2}}$

$\large\Longrightarrow\huge{\sf{x=\huge\frac{6+4}{2}}}$

$\large\Longrightarrow{\sf{x=\huge\frac{10}{2}}}$

$\large\therefore\boxed{\sf{x=5}}$

Now for y,

$\large\Longrightarrow{\sf{y=\huge\frac{y_1+y_2}{2}}}$

$\large\Longrightarrow{\sf{y=\huge\frac{2+(-4)}{2}}}$

$\large\Longrightarrow{\sf{y=\huge\frac{2-4}{2}}}$

$\large\Longrightarrow{\sf{y=\huge\frac{-2}{2}}}$

$\large\therefore\boxed{\sf{y=-1}}$

Therefore,

Coordinates of O(x, y) = (5, -1)

$\large\pink\therefore\boxed{\sf{\pink{Coordinates\:of\:O\:is\:(5,-1).}}}$