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