Videos and solutions to help Grade 8 students learn the characteristics of 180° rotations.

New York State Common Core Math Grade 8, Module 2, Lesson 6.

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Common Core For Grade 8

Student Outcomes

Students learn that a rotation of 180 degrees moves a point on the coordinate plane (a, b), to (-a, -b).

Students learn that a rotation of 180 degrees around a point, not on the line, produces a line parallel to the given line.

Example 1

The picture below shows what happens when there is a rotation of 180° around center O.

Example 2

The picture below shows what happens when there is a rotation of 180 around center O the origin of the coordinate plane.

Exercises

1. Using your transparency, rotate the plane 180 degrees, about the origin. Let this rotation be R_{O}. What are the coordinates of R_{O} (2, -4) ?

2. Let R_{O} be the rotation of the plane by 180 degrees, about the origin. Without using your transparency, find R_{O} (-3, 5).

3. Let R_{O} be the rotation of 180 degrees around the origin. Let L be the line passing through (-6, 6) parallel to the x-axis. Find R_{O} (L). Use your transparency if needed.

5. Let R

6. Let R

7. Let R

8. Let R

Lesson Summary

A rotation of 180 degrees around O is the rigid motion so that if P is any point in the plane P, O and Rotation (P) are collinear (i.e., lie on the same line).

Given a 180-degree rotation, R_{O} around the origin O of a coordinate system, and a point P with coordinates (a, b), it is generally said that R_{O}(P) is the point with coordinates (-a, -b).

**Theorem.** Let O be a point not lying on a given line L. Then the 180-degree rotation around O maps L to a line parallel to L.

9. Let R

Proof the Theorem: Let O be a point not lying on a given line L. Then the 180-degree rotation around O maps L to a line parallel to L.

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