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U9L3 Rotations Notes
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Name: Topic: Main Ideas/Questions ROTATIONS (about the origin) EXAMPLES Notes/Examples • A_TURN of 90° (counterclockwise) rotation • The figure rotates at a specific angle and direction Though the figure can rotate around any fixed point, the most common center of rotation is the origin. Rules for rotating points about the ORIGIN: 44 180° Date: 270° (counterclockwise) Class: around a fixed point called the center A': (-7,2) B': (-5,6) क्रैं (x,y) → (-X₁-y) 恰 (x,y) → (y₁ -x) Graph and label each figure and its image under the given rotation about the origin. Give the coordinates of the image. 1. Triangle ABC with vertices A(2, 7), 2. Square PQRS with vertices B(6,5), and C(4, 1): 90° counterclockwise c': (-1,4) (x,y) → (-y, x) P(2, 6), Q(6, 5), R(5, 1), and S(1, 2): 180° P': (-2,-6) 2: (-4,-5) ↑ R': (-5, -1) S: (-1,-2) ⒸGina Wilson (All Things Algebra, LLC), 2015-2018 3. Trapezoid JKLM with vertices J(3, 4), K(6, 4), L(8, 1), and M(1, 1): 270° counterclockwise J': (4, -3) K': (4,-6) L': (1,-8) M': (1,-1) 5. Rhombus CDEF with vertices C(-5, 5), D(-1, 7), E(-3, 3), and F(-7, 1): 270° counterclockwise C': (5,5) E': (3,3) D': (7,1) F': (1,7) 7. Parallelogram MNOP with vertices M(1,7), N(8, 5), O(4, 2), and P(-3, 4): 180° M': (-1,-1) 0': (-4,-2) N': (-8₁-5) P': (3,-4) 4. Triangle XYZ with vertices X(3,-2), Y(6, 1), and Z(5.-7): 180° X': (-3,2) z': (-5, 7) Y': (-6, -1) 6. Rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2,-8), and W(-5, -7): 90° counterclockwise T': (1₁-3) U': (2,0) 8. Triangle GHI with vertices G(0, -2), H(7,-6), and I(3,-8): 270° counterclockwise A I' v': (8,-2) W: (1,-5) G': (-2,0) H': (-6,-1) I': (-8,-3) Ⓒ...
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Alternative transcript:
Gina Wilson (All Things Algebra, LLC), 2015-2018 Clockwise EXAMPLES HINT: Think of the corresponding counterclockwise rotation and apply that rule. 9. Square ABCD with vertices A(-7, 5), B(-4, 7), C(-2, 4), and D(-5, 2): 90° counterclockwise A': (-5,-7) (-4,-2) B': (-7,-4) D': (-2,-5) 11. Triangle DEF with vertices D(4, 5), E(6, -2), and F(1, -2): 270° counterclockwise D': (5,-4) F: (-2,-1) E': (-2,-6) 13. Triangle LMN with vertices L(1,5), M(3, 8), and N(8, 1): 90° clockwise (210° ccw) 4 M N' L': (5,-1) N': (1,-8) M': (8,-3) 10. Rectangle WXYZ with vertices W(-3, -5), X(1, -1), Y(3,-3), and Z(-1,-7): 180° W': (3,5) X': (-1, 1) 12. Trapezoid RSTU with vertices R(-6, 7),S(-3, 5), T(-2, 0), and U(-8, 4): 180° u I Y': (-3,3) z': (1,7) R': (6,-7) S: (3,-5) T': (2,0) U': (8,-4) 14. Rhombus GHIJ with vertices G(-7, 2), H(-5, 6), I(-1,8), and J(-3, 4): 270° clockwise (90°cew] 4 G': (-2,-1) H': (-6,-5) И I': (-8,-1) J': (-4,-3) Ⓒ Gina Wilson (All Things Algebra®, LLC), 2015-2018
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Name: Topic: Main Ideas/Questions ROTATIONS (about the origin) EXAMPLES Notes/Examples • A_TURN of 90° (counterclockwise) rotation • The figure rotates at a specific angle and direction Though the figure can rotate around any fixed point, the most common center of rotation is the origin. Rules for rotating points about the ORIGIN: 44 180° Date: 270° (counterclockwise) Class: around a fixed point called the center A': (-7,2) B': (-5,6) क्रैं (x,y) → (-X₁-y) 恰 (x,y) → (y₁ -x) Graph and label each figure and its image under the given rotation about the origin. Give the coordinates of the image. 1. Triangle ABC with vertices A(2, 7), 2. Square PQRS with vertices B(6,5), and C(4, 1): 90° counterclockwise c': (-1,4) (x,y) → (-y, x) P(2, 6), Q(6, 5), R(5, 1), and S(1, 2): 180° P': (-2,-6) 2: (-4,-5) ↑ R': (-5, -1) S: (-1,-2) ⒸGina Wilson (All Things Algebra, LLC), 2015-2018 3. Trapezoid JKLM with vertices J(3, 4), K(6, 4), L(8, 1), and M(1, 1): 270° counterclockwise J': (4, -3) K': (4,-6) L': (1,-8) M': (1,-1) 5. Rhombus CDEF with vertices C(-5, 5), D(-1, 7), E(-3, 3), and F(-7, 1): 270° counterclockwise C': (5,5) E': (3,3) D': (7,1) F': (1,7) 7. Parallelogram MNOP with vertices M(1,7), N(8, 5), O(4, 2), and P(-3, 4): 180° M': (-1,-1) 0': (-4,-2) N': (-8₁-5) P': (3,-4) 4. Triangle XYZ with vertices X(3,-2), Y(6, 1), and Z(5.-7): 180° X': (-3,2) z': (-5, 7) Y': (-6, -1) 6. Rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2,-8), and W(-5, -7): 90° counterclockwise T': (1₁-3) U': (2,0) 8. Triangle GHI with vertices G(0, -2), H(7,-6), and I(3,-8): 270° counterclockwise A I' v': (8,-2) W: (1,-5) G': (-2,0) H': (-6,-1) I': (-8,-3) Ⓒ...
Name: Topic: Main Ideas/Questions ROTATIONS (about the origin) EXAMPLES Notes/Examples • A_TURN of 90° (counterclockwise) rotation • The figure rotates at a specific angle and direction Though the figure can rotate around any fixed point, the most common center of rotation is the origin. Rules for rotating points about the ORIGIN: 44 180° Date: 270° (counterclockwise) Class: around a fixed point called the center A': (-7,2) B': (-5,6) क्रैं (x,y) → (-X₁-y) 恰 (x,y) → (y₁ -x) Graph and label each figure and its image under the given rotation about the origin. Give the coordinates of the image. 1. Triangle ABC with vertices A(2, 7), 2. Square PQRS with vertices B(6,5), and C(4, 1): 90° counterclockwise c': (-1,4) (x,y) → (-y, x) P(2, 6), Q(6, 5), R(5, 1), and S(1, 2): 180° P': (-2,-6) 2: (-4,-5) ↑ R': (-5, -1) S: (-1,-2) ⒸGina Wilson (All Things Algebra, LLC), 2015-2018 3. Trapezoid JKLM with vertices J(3, 4), K(6, 4), L(8, 1), and M(1, 1): 270° counterclockwise J': (4, -3) K': (4,-6) L': (1,-8) M': (1,-1) 5. Rhombus CDEF with vertices C(-5, 5), D(-1, 7), E(-3, 3), and F(-7, 1): 270° counterclockwise C': (5,5) E': (3,3) D': (7,1) F': (1,7) 7. Parallelogram MNOP with vertices M(1,7), N(8, 5), O(4, 2), and P(-3, 4): 180° M': (-1,-1) 0': (-4,-2) N': (-8₁-5) P': (3,-4) 4. Triangle XYZ with vertices X(3,-2), Y(6, 1), and Z(5.-7): 180° X': (-3,2) z': (-5, 7) Y': (-6, -1) 6. Rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2,-8), and W(-5, -7): 90° counterclockwise T': (1₁-3) U': (2,0) 8. Triangle GHI with vertices G(0, -2), H(7,-6), and I(3,-8): 270° counterclockwise A I' v': (8,-2) W: (1,-5) G': (-2,0) H': (-6,-1) I': (-8,-3) Ⓒ...
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iOS User
I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D
Stefan S, iOS User
The application is very simple and well designed. So far I have found what I was looking for :D
SuSSan, iOS User
Love this App ❤️, I use it basically all the time whenever I'm studying
Alternative transcript:
Gina Wilson (All Things Algebra, LLC), 2015-2018 Clockwise EXAMPLES HINT: Think of the corresponding counterclockwise rotation and apply that rule. 9. Square ABCD with vertices A(-7, 5), B(-4, 7), C(-2, 4), and D(-5, 2): 90° counterclockwise A': (-5,-7) (-4,-2) B': (-7,-4) D': (-2,-5) 11. Triangle DEF with vertices D(4, 5), E(6, -2), and F(1, -2): 270° counterclockwise D': (5,-4) F: (-2,-1) E': (-2,-6) 13. Triangle LMN with vertices L(1,5), M(3, 8), and N(8, 1): 90° clockwise (210° ccw) 4 M N' L': (5,-1) N': (1,-8) M': (8,-3) 10. Rectangle WXYZ with vertices W(-3, -5), X(1, -1), Y(3,-3), and Z(-1,-7): 180° W': (3,5) X': (-1, 1) 12. Trapezoid RSTU with vertices R(-6, 7),S(-3, 5), T(-2, 0), and U(-8, 4): 180° u I Y': (-3,3) z': (1,7) R': (6,-7) S: (3,-5) T': (2,0) U': (8,-4) 14. Rhombus GHIJ with vertices G(-7, 2), H(-5, 6), I(-1,8), and J(-3, 4): 270° clockwise (90°cew] 4 G': (-2,-1) H': (-6,-5) И I': (-8,-1) J': (-4,-3) Ⓒ Gina Wilson (All Things Algebra®, LLC), 2015-2018