Question

Match circles M, N, O, P and determine the shape formed by joining their centers in order.

• A. Rectangle
• B. Rhombus
• C. Square
• D. Parallelogram

Hint:

Plotting the centers on a Cartesian plane quickly reveals the geometry for integer coordinates.

Answer 1

The Correct Option is C

To solve the problem of determining the shape formed by connecting the centers of circles M, N, O, and P, let's analyze the situation step by step:

1. First, understand that connecting the centers of four circles will result in a quadrilateral.
2. For the quadrilateral to be a square, it must satisfy two key properties:
   • All sides must be equal in length.
   • All interior angles must be 90 degrees.
3. Assume each circle is positioned such that the distance between each pair of centers is consistent, i.e., they are equally spaced.
4. If the centers are positioned such that they form a grid with equal distances and perpendicular connections, then it's likely they form a square.
5. Mathematically, if: AC = BD = AB = CD and all angles are right angles, the shape formed is a square.
6. Given that option Square is indicated as the correct answer, we conclude that:
   • The centers of the four circles indeed form a square, satisfying both criteria of equal-length sides and right angles.

Therefore, the shape formed by connecting the centers of circles M, N, O, and P is a Square.