Math Problem Statement

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

Solution

To solve this problem, we need to understand how to apply a 180° rotation about the origin to the given point on the graph.

Step-by-step process:

  1. Locate the initial coordinates of point A: From the graph, point A appears to be at the coordinates (3, 5).

  2. Apply the 180° rotation rule:

    • When rotating a point 180° around the origin, the coordinates (x,y)(x, y) are transformed into (x,y)(-x, -y).

    So, the new coordinates of AA' will be: A=(3,5)A' = (-3, -5)

Conclusion:

The correct coordinate of AA' after a 180° rotation is (-3, -5).

Do you want more details or have any questions?

Here are 5 related questions to expand on this topic:

  1. What is the rule for rotating a point 90° counterclockwise about the origin?
  2. How does the coordinate transformation change for a 270° rotation?
  3. How do you reflect a point over the x-axis, and what is the resulting coordinate?
  4. Can you explain how translations differ from rotations in geometry?
  5. What is the effect of a 360° rotation on any given point?

Tip: When rotating a figure, always pay attention to whether the rotation is clockwise or counterclockwise, as this will affect how the coordinates are transformed!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Transformations
Rotation

Formulas

(x, y) -> (-x, -y) for 180° rotation

Theorems

Rotation theorem

Suitable Grade Level

Grades 7-9