g8-m2-lesson 6: rotations of 180 degrees - mod 2...2015-16 lesson 6 : rotations of 180 degrees 8β’2...
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.
Β© 2015 Great Minds eureka-math.org G8-M2-HWH-1.3.0-09.2015
10
Homework Helper A Story of Ratios
2015-16
Lesson 6: Rotations of 180 Degrees
8β’2
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.
Β© 2015 Great Minds eureka-math.org G8-M2-HWH-1.3.0-09.2015
11
Homework Helper A Story of Ratios