The centre of a circle is \(C(-2,\,3)\). One end of a diameter of the circle is \(A(5,\,-1)\). What are the coordinates of the other end of this diameter?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \((-9,\,7)\)
The centre of a circle is the mid-point of every diameter. So if the other end is \(B(x,\,y)\), the mid-point of AB is \(C(-2,\,3)\).
x-coordinate: \(\displaystyle \frac{5+x}{2}=-2\), so \(5+x=-4\) and \(x=-9\)
y-coordinate: \(\displaystyle \frac{-1+y}{2}=3\), so \(-1+y=6\) and \(y=7\)
The other end is \(B(-9,\,7)\)
