AB is a diameter of a circle with centre (3, 4). If coordinates of A is the point (4, 9), then find the coordinates of B.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (2, −1)
The centre of a circle is the midpoint of every diameter, so the centre (3, 4) is halfway between A (4, 9) and B \((x,y)\). By the midpoint formula, each coordinate of the centre is the average of those of A and B.
\(\displaystyle\frac{4+x}{2}=3\), so \(4+x=6\) and \(x=2\)
\(\displaystyle\frac{9+y}{2}=4\), so \(9+y=8\) and \(y=-1\)
