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Q.

What are the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4)?
 


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a

(5,6)

b

(3,8)

c

(3,-10)

d

(3,-1) 

answer is C.

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Detailed Solution

Given that AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).
We know that the centre of a circle is the midpoint of the diameter of the circle.
Let the coordinates of A be (p, q).
Coordinates of centre O are (2,-3), coordinates of B are (1,4).
Question Image
We know that midpoint formula is given by
M(x, y) = [ x 1 + x 2 2 , y 1 + y 2 2 ]  .
Using midpoint theorem, we get
1+p 2 =2, 4+q 2 =−3  
1+p=4,4+q=−6 p=3,q=−10  
The coordinates of point A are (3, -10).
Therefore, the correct option is 3.
 
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