Question

Q13. The coordinate of one end point of a diameter of a circle are (4,-1)and the coordinate of the centre of the circle are (1,-3).Find the coordinate of the other end of the diameter .
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Answer 1

Given :–

• One end point of a diameter of a circle are (4, –1).
• The coordinate of the centre of the circle are (1, –3).

To Find :–

• The coordinate of the other end of the diameter.

Solution :–

Let, the diameter of the circle centre be C.

The co-ordinate of the one end of the diameters of the circle be A.

The co-ordinate of the other end of the diameter of the circle be B.

And,

• C = (1, –3)

So,

We need to find B which is the other end of the diameter AB.

C is the mid-point of AB.

So,

(1, –3) = $( \dfrac{x + 4}{2}, \dfrac{-1 + y}{2})$

So,

• $\dfrac{x + 4}{2}$ = 1

⟹ x + 4 = 2

⟹ x = 2 – 4

⟹ x = –2

And,

• $\dfrac{-1 + y}{2}$ = –3

⟹ –1 + y = –3 × 2

⟹ y = –6 + 1

⟹ y = –5

Hence,

The co-ordinates of the other end of the diameter (B) = (–2, –5).