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F the Coordinates of One End of a Diameter of a Circle Are (2, 3) and the Coordinates of Its Centre Are (−2, 5), Then the Coordinates of the Other End of the Diameter Are

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प्रश्न

f the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are

 

विकल्प

  •  (−6, 7)    

  •  (6, −7)      

  •  (6, 7)      

  • (−6,−7)       

MCQ
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उत्तर


Let O(−2, 5) be the centre of the given circle and A(2, 3) and B(xy) be the end points of a diameter of the circle.

Then, O is the mid-point of AB.

Using mid-point formula, we have

\[\therefore \frac{2 + x}{2} = - 2\]  and  \[\frac{3 + y}{2} = 5\]
\[\Rightarrow 2 + x = - 4\]  and \[3 + y = 10\]
 
\[\Rightarrow x = - 6\]  and  \[y = 7\]
 
Thus, the coordinates of the other end of the diameter are (−6, 7).
Hence, the correct answer is option A.
 
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अध्याय 6: Co-ordinate Geometry - Exercise 6.7 [पृष्ठ ६६]

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आर.डी. शर्मा Mathematics [English] Class 10
अध्याय 6 Co-ordinate Geometry
Exercise 6.7 | Q 41 | पृष्ठ ६६

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