If the coordinates of one end of a diameter of a circle are $(2, 3)$ and the center is $( -2, 5)$, then the coordinates of the other end are:
1 mark
🔍 View Detailed Solution & Schema →

Question

If the coordinates of one end of a diameter of a circle are $(2, 3)$ and the center is $( -2, 5)$, then the coordinates of the other end are:

Accepted Answer

Let the other end be $(x, y)$. Since the center is the midpoint of the diameter, we can write $\frac{2 + x}{2} = -2$ and $\frac{3 + y}{2} = 5$. Solving for x: $2 + x = -4 \implies x = -6$. Solving for y: $3 + y = 10 \implies y = 7$. Thus, the coordinates are $(-6, 7)$. Therefore, the correct option is A.

Coordinate Geometry

❓ Sibling Questions in this Chapter