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Question

The co-ordinates of one end of a diameter of a circle are (5,7). If the co-ordinates of the centre be (7,3), the co-ordinates of the other end of the diameter are:

A
(6,2)
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B
(9,13)
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C
(2,6)
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D
(13,9)
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Solution

The correct option is B (9,13)
The centre of the circle lies at the mid point of the diameter.
Let the other end of the diameter be (x,y)
Midpoint of two points (x1,y1) and (x2,y2) is calculated by the formula (x1+x22,y1+y22)
Using this formula, mid point of (x,y)and(5,7)=(x+52,y72)
So,(x+52,y72)=(7,3)

=>x+5=7×2 and y7=3×2
=>x=9;y=13
Thus, the other end of the diameter is (9,13).

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