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Questions and Answers
What is the new position of vertex T after the 90° counterclockwise rotation of trapezoid STUV?
What is the new position of vertex T after the 90° counterclockwise rotation of trapezoid STUV?
What is the new position of vertex L after the dilation of triangle LMN with a scale factor of 2?
What is the new position of vertex L after the dilation of triangle LMN with a scale factor of 2?
What is the new position of vertex D after the dilation of square CDEF with a scale factor of 1/3?
What is the new position of vertex D after the dilation of square CDEF with a scale factor of 1/3?
What is the new position of vertex R after the dilation of triangle QRS with a scale factor of 5/2?
What is the new position of vertex R after the dilation of triangle QRS with a scale factor of 5/2?
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What type of transformation is described in problem 12?
What type of transformation is described in problem 12?
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What is the transformation applied to Triangle GHI with vertices G(-8, 3), H(0, 7), and I(-4, 1) in question 5?
What is the transformation applied to Triangle GHI with vertices G(-8, 3), H(0, 7), and I(-4, 1) in question 5?
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What are the coordinates of vertex B' after applying a 270° counterclockwise rotation to Parallelogram ABCD in question 6?
What are the coordinates of vertex B' after applying a 270° counterclockwise rotation to Parallelogram ABCD in question 6?
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Which transformation is applied to Rectangle WXYZ with vertices W(-4, 2), X(5, 5), Y(7, -1), and Z(-2, -4) in question 4?
Which transformation is applied to Rectangle WXYZ with vertices W(-4, 2), X(5, 5), Y(7, -1), and Z(-2, -4) in question 4?
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What are the coordinates of vertex Q' after reflecting Rhombus QRST with vertices Q(-6, -2), R(0, -1), S(-1, -7), and T(-7, -8) in the y-axis in question 2?
What are the coordinates of vertex Q' after reflecting Rhombus QRST with vertices Q(-6, -2), R(0, -1), S(-1, -7), and T(-7, -8) in the y-axis in question 2?
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For Triangle DEF with vertices D(1, -3), E(8, -2), and F(3, -7), what are the coordinates of vertex F' after reflecting in the x-axis in question 1?
For Triangle DEF with vertices D(1, -3), E(8, -2), and F(3, -7), what are the coordinates of vertex F' after reflecting in the x-axis in question 1?
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Study Notes
Transformations Review
- The review consists of 14 exercises on geometry transformations, including rotations, reflections, and dilations.
Exercise 1: Reflection in the y-axis
- The transformation is applied to Triangle DEF with vertices D(1, -3), E(8, -2), and F(3, -7).
- The new coordinates are: D'(-1, -3), E'(-8, -2), and F'(-3, -7).
Exercise 2: Reflection in the x-axis
- The transformation is applied to Rhombus QRST with vertices Q(-6, -2), R(0, -1), S(7, -2), and T(1, -1).
- The new coordinates are: Q'(-6, 2), R'(0, 1), S'(7, 2), and T'(1, 1).
Exercise 3: Translation
- The transformation is applied to Quadrilateral JKLM with vertices J(-5, 5), K(2, -1), L(-5, 0), and M(-6, 2).
- The rule is (x, y) → (x + 5, y – 7).
- The new coordinates are: J' (0, -2), K' (7, -8), L' (0, -7), and M' (-1, -5).
Exercise 4: Translation
- The transformation is applied to Rectangle WXYZ with vertices W(-4, 2), X(5, 5), Y(7, -1), and Z(-2, -4).
- The rule is (x, y) → (x – 4, y – 3).
- The new coordinates are: W'(-8, -1), X'(1, 2), Y'(3, -4), and Z'(-6, -7).
Exercise 5: Rotation
- The transformation is a 180° rotation applied to Triangle GHI with vertices G(-8, 3), H(0, 7), and I(-4, 1).
- The new coordinates are: G'(8, -3), H'(0, -7), and I'(4, -1).
Exercise 6: Rotation
- The transformation is a 270° counterclockwise rotation applied to Parallelogram ABCD with vertices A(5, -2), B(8, -1), C(5, -6), and D(2, -7).
- The new coordinates are: A'(-5, -2), B'(-8, -1), C'(-5, -6), and D'(-2, -7).
Exercise 7: Rotation
- The transformation is a 90° counterclockwise rotation applied to Trapezoid STUV with vertices S(-7, -2), T(-5, -1), U(0, -3), and V(-6, -6).
- The new coordinates are: S'(-5, -6), T'(-3, -5), U'(-1, -2), and V'(-5, -3).
Exercise 8: Dilation
- The transformation is a dilation with scale factor k = 2 applied to Triangle LMN with vertices L(2, 7), M(6, 0), and N(3, 1).
- The new coordinates are: L'(4, 14), M'(12, 0), and N'(6, 2).
Exercise 9: Dilation
- The transformation is a dilation with scale factor k = 1/3 applied to Square CDEF with vertices C(-12, 3), D(-3, 0), E(-6, -9), and F(-15, -6).
- The new coordinates are: C'(-4, 1), D'(-1, 0), E'(-2, -3), and F'(-5, -2).
Exercise 10: Dilation
- The transformation is a dilation with scale factor k = 5/2 applied to Triangle QRS with vertices Q(2, -4), R(6, -2), and S(4, -6).
- The new coordinates are: Q'(5, -10), R'(15, -5), and S'(10, -15).
Exercise 11-14: Various Transformations
- The transformations and their respective figures are not specified.
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Description
Practice graphing and labeling figures and their images under given transformations. Calculate the new coordinates after each transformation, including reflections and rotations around the origin. This homework sheet contains two pages of exercises.
