Rotate 180° Around the Origin

🔑 Key Concepts

  • A rotation turns a figure around a fixed point called the origin.
  • A 180° rotation around the origin changes each point from \(x,y\) to \(-x,-y\).
  • The rotated figure will be the same size and shape as the original figure.
  • The signs of both coordinates change during a 180° rotation around the origin.

💡 Main Idea

To rotate a figure 180° around the origin, change the sign of both coordinates. In coordinate rule form, \(x,y\) becomes \(-x,-y\). This means a point in Quadrant II will move to Quadrant IV, and a point in Quadrant I will move to Quadrant III. A rotation preserves the size and shape of the figure while changing its position on the coordinate plane.

📚 What You Should Already Know

Students should already know how to plot ordered pairs on the coordinate plane, identify the x-axis and y-axis, and read coordinates correctly as \(x,y\). Students should also understand that the sign of a coordinate tells whether a point is above or below the x-axis or left or right of the y-axis. In addition, students should know the names and locations of the four quadrants — Quadrant I, Quadrant II, Quadrant III, and Quadrant IV — and understand the sign patterns of coordinates in each quadrant.

🚀 What Comes Next

After learning how to rotate figures 180° around the origin, students can extend this idea to rotations of 90° and 270°, rotations in clockwise and counterclockwise directions, and sequences of transformations that combine rotations, reflections, and translations. These concepts help build a deeper understanding of congruence and geometric transformations on the coordinate plane.

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