Question

3) The coordinates of diameter AB of a circle are A (2,7) and
B (4,5) then find the coordinates of the centre.
Answer :

Step - by - step explanation : ​

Answer 1

Step-by-step explanation:

the explanation is given

Answer 2

Topic :-

Coordinate Geometry

Given :-

The coordinates of diameter AB of a circle are A (2, 7) and  B (4, 5).

To Find :-

The coordinates of the centre.

Concept Used :-

Centre of circle is present at the mid of diameter of the circle.

The coordinate of mid-point of a line AB with A (x₁, y₁) and B (x₂, y₂) is given by :-

$\sf {(x,y) \equiv \left (\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right )}$

Solution :-

As we know, centre of circle is present at the mid of diameter of the circle.

So, centre of circle with coordinates of its diameter as A (2, 7) and B (4, 5) will lie on mid of AB.

Assuming,

A (2, 7) ≡ (x₁, y₁)

A (4, 5) ≡ (x₂, y₂)

Using formula to calculate mid-point of line AB,

$\sf {(x,y) \equiv \left (\dfrac{2+4}{2},\dfrac{7+5}{2}\right )}$

$\sf {(x,y) \equiv \left (\dfrac{6}{2},\dfrac{12}{2}\right )}$

$\sf {(x,y) \equiv \left (3,6\right )}$

Answer :-

So, coordinates of centre of given circle is (3, 6).

Note : Refer to attachment for better understanding.