-y x ** 9 1 -x - 5 -5 y -x -1 7
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Aim 13d rotations in the coordinate plane.notebook 1 December 07, 2015 Dec 311:11 PM Aim 13d: How do we rotate coordinates on a graph (rules)? Do Now: Use the examples below to complete the rules for Rotations whose center is the origin. -y x y -x -x -y Remember that a rotation of 90 ccw gets you to the same place as 270 cw Remember that a rotation of 180 ccw gets you to the same place as 180 cw Remember that a rotation of 270 ccw gets you to the same place as 90 cw 5 1 9 1 ** 5 -5 -1 -5 -1 7 Dec 311:12 PM Aim 13d: How do we rotate coordinates on a graph (rules)? 2 3 2 5 4 6 5 4 4 2 -3 2 -5 2 -6 4 -4 5 -2 4 P' P'' Q' v Q'' R' R'' S' S'' T' T'' ccw
Transcript of -y x ** 9 1 -x - 5 -5 y -x -1 7
Aim 13d rotations in the coordinate plane.notebook
1
December 07, 2015
Dec 311:11 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Do Now: Use the examples below to complete the rules for Rotations whose center is the origin.
-y x
y -x
-x -y
Remember that a rotation of 90 ccw gets you to the same place as 270 cw
Remember that a rotation of 180 ccw gets you to the same place as 180 cw
Remember that a rotation of 270 ccw gets you to the same place as 90 cw
5 19 1**
5 -5-1 -5-1 7
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Aim 13d: How do we rotate coordinates on a graph (rules)?
2 3
2 5
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5 4
4 2
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-4 5
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P'P''
Q'
v
Q''
R'
R'' S'
S''
T'
T''
ccw
Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
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Aim 13d: How do we rotate coordinates on a graph (rules)?
4. CHALLENGE: Point C has coordinates C(5, 5). The image of this point after a rotation of 100° about a certain point is C′(5, 7.5). Find the coordinates of the center of this rotation. (Hint: To be precise use each box as )
1 2 3 4 5-1-2-3-4-5
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c
c'
0°249
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
4. CHALLENGE: Point C has coordinates C(5, 5). The image of this point after a rotation of 100° about a certain point is C′(5, 7.5). Find the coordinates of the center of this rotation. (Hint: To be precise use each box as )
1 2 3 4 5-1-2-3-4-5
1
2
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7
8
c
c'
0°249
Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
4. CHALLENGE: Point C has coordinates C(5, 5). The image of this point after a rotation of 100° about a certain point is C′(5, 7.5). Find the coordinates of the center of this rotation. (Hint: To be precise use each box as )
1 2 3 4 5-1-2-3-4-5
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c
c'
There are 3 points you can guess. Now make the angle and check which one is 100 degrees
0°249
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
4. CHALLENGE: Point C has coordinates C(5, 5). The image of this point after a rotation of 100° about a certain point is C′(5, 7.5). Find the coordinates of the center of this rotation. (Hint: To be precise use each box as )
1 2 3 4 5-1-2-3-4-5
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7
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c
c'
The coordinate (-1,2) makes and angle of rotation of 100 degrees.
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Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
4. CHALLENGE: Point C has coordinates C(5, 5). The image of this point after a rotation of 100° about a certain point is C′(5, 7.5). Find the coordinates of the center of this rotation. (Hint: To be precise use each box as )
1 2 3 4 5-1-2-3-4-5
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2
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c
c'
There are 3 points you can guess. Now make the angle and check which one is 100 degrees
0°249
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Aim 13d: How do we rotate coordinates on a graph (rules)?
5. Are collinearity and betweenness of points maintained under rotation? (You can make up an example with the extra space on the graph.)
Explain.Collinear points are points on the same line. So if I rotate collinear points will the image points still be colliner? Betweenness looks like the partition postulate. For example, If AB+BC=AC , then B is between A and C. So rotate 90 degrees and If A'B'+B'C'=A'C'then will B' still be between A' and C'? The answers to both questions is YES, since rotations are a rigid motion which produces a congruent shape. So the segments drawn in each case will produce congruent segments when rotated.
Aim 13d rotations in the coordinate plane.notebook
5
December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
For queson 7 & 8, Locate the center of rotation P, then find the angle of rotation.6)
point is center of rotation since it is invariant (does not move).
P
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
For queson 7 & 8, Locate the center of rotation P, then find the angle of rotation.6)
Rotation ccw 82°P
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Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
For queson 7 & 8, Locate the center of rotation P, then find the angle of rotation.7)
0°
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Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
For queson 7 & 8, Locate the center of rotation P, then find the angle of rotation.7)
0° 168
Aim 13d rotations in the coordinate plane.notebook
7
December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
For queson 7 & 8, Locate the center of rotation P, then find the angle of rotation.7)
•P0° 168
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
For queson 7 & 8, Locate the center of rotation P, then find the angle of rotation.7)
•P0° 168
Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
For queson 7 & 8, Locate the center of rotation P, then find the angle of rotation.7) cw,
obtuse122°
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RP,122°•P
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d rotations in the coordinate plane.notebook
10
December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
••
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Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
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Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
• •T'
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Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
••
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Aim 13d rotations in the coordinate plane.notebook
12
December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d rotations in the coordinate plane.notebook
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December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Aim 13d rotations in the coordinate plane.notebook
16
December 07, 2015
Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
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Dec 311:12 PM
Aim 13d: How do we rotate coordinates on a graph (rules)?
10. Def: An invariant point of a function is an element of the function's domain that is mapped to itself. Do invariant points sometimes, always, or never occur in a rotation? Explain your reasoning.
If the center of rotation is a point on the shape being rotated, then it does not move. Therefore it is an invariant point.
