Math Problem Statement

If you were to rotate ABCD 180° about the origin, what would the coordinate of A' be?

Solution

To determine the coordinates of point AA' after rotating point AA 180° about the origin, we can use the rule for 180° rotation in the coordinate plane. When a point (x,y)(x, y) is rotated 180° about the origin, its coordinates become (x,y)(-x, -y).

Looking at the grid, let's assume the coordinates of point AA (we'd need to read them from the grid in the image). If, for instance, AA is at (x,y)(x, y), then AA' would be located at (x,y)(-x, -y).

Once we identify the coordinates of AA, we can find the correct answer among the given options:

  • (-5, 3)
  • (-3, -5)
  • (-5, 5)
  • (-3, 3)

If you can specify the initial coordinates of point AA, I can provide the exact rotated position. Would you like me to go into more details about the rotation process?

Related Questions:

  1. What is the rule for rotating points by 90° around the origin?
  2. How does rotating a point 270° differ from rotating it 90°?
  3. How would you find the new position of a point after a 360° rotation?
  4. What changes in coordinates occur when rotating around a point other than the origin?
  5. How would you apply this to other quadrilaterals like a rectangle?

Tip: For any 180° rotation around the origin, simply negate both coordinates.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Rotation Transformation

Formulas

180° Rotation about the Origin: (x, y) -> (-x, -y)

Theorems

Rotation Theorem

Suitable Grade Level

Grades 8-10