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Lesson Plans and Worksheets for Grade 8

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Common Core For Grade 8

Examples, 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

Worksheets and solutions for Common Core Grade 8, Module 2, Lesson 6

Student Outcomes

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

5. Let R_{O} 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 R_{O} (L)?

6. Let R_{O} 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 R_{O} (L)?

7. Let R_{O} 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 R_{O} (L)?

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

9. Let R_{O} be the rotation of degrees around the origin. Is L parallel to R_{O}(L)? Use your transparency if needed.

**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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn the characteristics of 180° rotations.

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

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.

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).

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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