G8-M2-Lesson 6: Rotations of 180 Degrees - Mod 2...2015-16 Lesson 6 : Rotations of 180 Degrees 8β’2 1. Looking only at segment π΅π΅π΅π΅, is it possible that a 180 rotation
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Transcript
2015-16
Lesson 6: Rotations of 180 Degrees
8β’2
G8-M2-Lesson 6: Rotations of 180 Degrees
Lesson Notes
When a line is rotated 180Β° around a point not on the line, it maps to a line parallel to the given line. A point ππ with a rotation of 180Β° around a center ππ produces a point ππβ² so that ππ, ππ, and ππβ²are collinear. When we rotate coordinates 180Β° around ππ, the point with coordinates (ππ, ππ) is moved to the point with coordinates (βππ,βππ).
Example
Use the following diagram for Problems 1β5. Use your transparency as needed.
1. Looking only at segment π΅π΅π΅π΅, is it possible that a 180Β° rotation would map segment π΅π΅π΅π΅ onto segment π΅π΅β²π΅π΅β²? Why or why not?
It is possible because the segments are parallel.
2. Looking only at segment π΄π΄π΅π΅, is it possible that a 180Β° rotation
would map segment π΄π΄π΅π΅ onto segment π΄π΄β²π΅π΅β²? Why or why not?
It is possible because the segments are parallel.
3. Looking only at segment π΄π΄π΅π΅, is it possible that a 180Β° rotation would map segment π΄π΄π΅π΅ onto segment
π΄π΄β²π΅π΅β²? Why or why not?
It is possible because the segments are parallel.
4. Connect point π΅π΅ to point π΅π΅β², point π΅π΅ to point π΅π΅β², and point π΄π΄ to
point π΄π΄β². What do you notice? What do you think that point is?
All of the lines intersect at one point. The point is the center of rotation. I checked by using my transparency.
5. Would a rotation map β³ π΄π΄π΅π΅π΅π΅ onto β³ π΄π΄β²π΅π΅β²π΅π΅β²? If so, define the
rotation (i.e., degree and center). If not, explain why not.
Let there be a rotation of ππππππΒ° around point (ππ,ππ). Then, πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ(β³π¨π¨π¨π¨π¨π¨) =β³ π¨π¨β²π¨π¨β²π¨π¨β².
I will use my transparency to verify that the segments are parallel. I think the center of rotation is the point (2, 6).
I checked each segment and its rotated segment to see if they were parallel. I found the center of rotation, so I can say there is a rotation of 180Β° about a center.