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Rotations of 180 Degrees




 


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.

Related Topics:
Lesson Plans and Worksheets for Grade 8

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More Lessons for Grade 8

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 RO. What are the coordinates of RO (2, -4) ?

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

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

4. Let RO be the rotation of 180 degrees around the origin. Let L be the line passing through (7, 0) parallel to the y-axis. Find RO (L). Use your transparency if needed.

5. Let RO be the rotation of 180 degrees around the origin. Let L be the line passing through (0, 2) parallel to the x-axis. Is L parallel to RO (L)?

6. Let RO be the rotation of 180 degrees around the origin. Let L be the line passing through (4, 0) parallel to the y-axis. Is L parallel to RO (L)?

7. Let RO be the rotation of 180 degrees around the origin. Let L be the line passing through (0, -1) parallel to the x-axis. Is L parallel to RO (L)?

8. Let RO be the rotation of 180 degrees around the origin. Is L parallel to RO (L)? Use your transparency if needed.

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, RO around the origin O of a coordinate system, and a point P with coordinates (a, b), it is generally said that RO(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 RO be the rotation of degrees around the origin. Is L parallel to RO(L)? Use your transparency if needed.

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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