G8-M2-Lesson 6: Rotations of 180 Degrees - Mod 2...2015-16 Lesson 6 : Rotations of 180 Degrees 8•2...
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2015-16 Lesson 6: Rotations of 180 Degrees 8•2 G8-M2-Lesson 6: Rotations of 180 Degrees Lesson Notes When a line is rotated 180° around a point not on the line, it maps to a line parallel to the given line. A point with a rotation of 180° around a center produces a point ′ so that , , and ′are collinear. When we rotate coordinates 180° around , the point with coordinates (, ) is moved to the point with coordinates (−, −). Example Use the following diagram for Problems 1–5. Use your transparency as needed. © 2015 Great Minds eureka-math.org G8-M2-HWH-1.3.0-09.2015 10 Homework Helper A Story of Ratios
Transcript of G8-M2-Lesson 6: Rotations of 180 Degrees - Mod 2...2015-16 Lesson 6 : Rotations of 180 Degrees 8•2...
2015-16
Lesson 6: Rotations of 180 Degrees
8•2
G8-M2-Lesson 6: Rotations of 180 Degrees
Lesson Notes
When a line is rotated 180° around a point not on the line, it maps to a line parallel to the given line. A point 𝑃𝑃 with a rotation of 180° around a center 𝑂𝑂 produces a point 𝑃𝑃′ so that 𝑃𝑃, 𝑂𝑂, and 𝑃𝑃′are collinear. When we rotate coordinates 180° around 𝑂𝑂, the point with coordinates (𝑎𝑎, 𝑏𝑏) is moved to the point with coordinates (−𝑎𝑎,−𝑏𝑏).
Example
Use the following diagram for Problems 1–5. Use your transparency as needed.
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2015-16
Lesson 6: Rotations of 180 Degrees
8•2
1. Looking only at segment 𝐵𝐵𝐵𝐵, is it possible that a 180° rotation would map segment 𝐵𝐵𝐵𝐵 onto segment 𝐵𝐵′𝐵𝐵′? Why or why not?
It is possible because the segments are parallel.
2. Looking only at segment 𝐴𝐴𝐵𝐵, is it possible that a 180° rotation
would map segment 𝐴𝐴𝐵𝐵 onto segment 𝐴𝐴′𝐵𝐵′? Why or why not?
It is possible because the segments are parallel.
3. Looking only at segment 𝐴𝐴𝐵𝐵, is it possible that a 180° rotation would map segment 𝐴𝐴𝐵𝐵 onto segment
𝐴𝐴′𝐵𝐵′? Why or why not?
It is possible because the segments are parallel.
4. Connect point 𝐵𝐵 to point 𝐵𝐵′, point 𝐵𝐵 to point 𝐵𝐵′, and point 𝐴𝐴 to
point 𝐴𝐴′. 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 △ 𝐴𝐴𝐵𝐵𝐵𝐵 onto △ 𝐴𝐴′𝐵𝐵′𝐵𝐵′? If so, define the
rotation (i.e., degree and center). If not, explain why not.
Let there be a rotation of 𝟏𝟏𝟏𝟏𝟏𝟏° around point (𝟐𝟐,𝟔𝟔). Then, 𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹(△𝑨𝑨𝑨𝑨𝑨𝑨) =△ 𝑨𝑨′𝑨𝑨′𝑨𝑨′.
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 180° about a center.
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