Question

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (-2, 0) and B is (6, -4)

Answer 1

Step-by-step explanation:

Given :-

AB is the diameter of a circle whose centre is (-2, 0) and B is (6, -4).

To find :-

Find the coordinates of a point A ?

Solution :-

Given that

AB is the diameter of the circle .

Let the coordinates of the point A be (x,y)

B = (6,-4)

The coordinates of the centre of the circle = (-2,0)

It is clear that

The centre of the circle is the mid point of the diameter which passes through the centre .

We know that

The coordinates of the mid point of the linesegment joining the points (x1, y1) and (x2, y2) is ( (x1+x2)/2 , (y1+y2)/2 )

Let (x1,y1) = A (x,y) => x1 = x and y1 = y

Let (x2, y2) = B(6,-4) => x2 = 6 and y2 = -4

Mid point = ( ( x+6)/2 , (y-4)/2 )

=> ( ( x+6)/2 , (y-4)/2 ) = (-2,0)

On Comparing both sides then

=> (x+6)/2 = -2 and (y-4)/2 = 0

Now,

(x+6)/2 = -2

=> x+6 = -2×2

=> x+6 = -4

=> x = -4-6

=> x = -10

and

(y-4)/2 = 0

=> y-4 = 0×2

=> y-4 = 0

=> y = 0+4

=> y = 4

Therefore, (x,y) = (-10,4)

Answer:-

The coordinates of the point A = (-10,4)

Used formulae:-

→ The coordinates of the mid point of the linesegment joining the points (x1, y1) and (x2, y2) is ( (x1+x2)/2 , (y1+y2)/2 )

Used Concept:-

→ The diameter passes through the centre of the circle.

→ The centre divides the diameter into two equal parts.

→ The centre of the circle is the mid point of the diameter of the circle .