Question

If (0,0)is the centre of a circle and (2,3) is one endpoint of its diameter then find the other end point.
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Answer 1

Let AB be a diameter of the circle having its centre at C(1, -3) such that the coordinates of one end A are (4, -1).

Let the coordinates of B be (x,y).

Since C is the mid-point of AB. Therefore,the coordinates of C are(

2x+42y−1 ).

But, the coordinates of C are given to be (1,-3.∴

2x+4 =1

andy− =−3

⇒x+4=2andy−1=−6

⇒x=−2andy=−5

Hence,the coordinates of B are (-2, -5).

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Answer 2

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One end of diameter of the circle = (3,2)

Center of the circle = (0,0)

Let, the other end of diameter of the circle = (x,y)

Since , center is the mid-point of the diameter of the circle

• (0,0)=( 3+x / 2 , 2+y / 2)
• 23+x =0 and 22+y =0
• 3+x=0 and 2+y=0
• x=−3 and y=−2

Hence, the other end of diameter of the circle =(−3,−2)