Question

If (9,3) is one end point of the diameter of a circle whose centre is
(5,1). Then the other end point is --------
(A) (7,2)
(B) (2,1)
(C) (1,-1)
(D) (-2,-1)
​

Answer 1

$Given \: One \: end \: point \:of \: diameter\\A(x_{1},y_{1}) = (9,3) , Center \: of \:the \:circle \: O( 5,1 )$

$Let \: Other \: end \: point \: B(x_{2}, y_{2})$

$Mid \:point \: AB = O(5,1)$

$\implies \big( \frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\big) = O(5,1)$

$\implies \big( \frac{9+ x_{2}}{2}, \frac{3+y_{2}}{2}\big) = O(5,1)$

$\implies \frac{9+ x_{2}}{2}= 5; \: \frac{3+y_{2}}{2} = 1$

$\implies 9+ x_{2}= 10; \: 3+y_{2} = 2$

$\implies x_{2}= 10 - 9 ; \:y_{2} = 2 - 3$

$\implies x_{2}= 1; \:y_{2} = - 1$

$\red { Other \:end \: point } \green {= ( 1, -1) }$

Therefore.,

$Option \:\pink { ( C) }\: is \: correct.$

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