Geometry Unit 3 Rigid Transformations and Symmetry Note Sheets

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3.1 Reflections

Example 1: Reflect a Figure in a Line Draw the reflected image of quadrilateral WXYZ in line p using a ruler.

Guided Practice 1: Reflect a Figure in a Line Draw the reflected image of quadrilateral ABCD in line n.

Example 2: Minimize Distance Using a Reflection BILLIARDS Suppose that you must bounce the cue ball off side A before it rolls into the pocket at B. Locate the point C along side A that the ball must hit to ensure that it will roll directly toward the pocket.

Guided Practice 2: Minimize Distance Using a Reflection MINIATURE GOLF Omar is playing miniature golf at a local course. Because a wall is blocking his direct shot, he needs to bounce the ball off wall W and hit the hole located at point H. Which of these steps would be needed to determine where on wall W Omar should aim?

Geometry Unit 3 Rigid Transformations and Symmetry Note Sheets

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Example 3A: Reflect a Figure in a Vertical Line A. Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1). Graph JKLM and its reflection over x = 1.

Example 3B: Reflect a Figure in a Horizontal Line B. Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1). Graph JKLM and its reflection over y = –2.

Guided Practice 3A: Reflect a Figure in a Vertical Line Quadrilateral ABCD has vertices A(1, 2), B(0, 1), C(1, –2), and D(3, 0). Graph ABCD and its image over x = 2.

Guided Practice 3B Reflect a Figure in a Horizontal Line Quadrilateral WXYZ has vertices W(2, 4), X(3, 3), Y(2, 0), and Z(0, 2). Graph WXYZ and its image over y = –1.

Geometry Unit 3 Rigid Transformations and Symmetry Note Sheets

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Example 4A: Reflect a Figure in the x or y axis Given quadrilateral A(1, 1), B(3, 2), C(4, –1), and D(2, –3) and its image A′(1, –1), B′(3, –2), C′(4, 1), and D ′(2, 3), describe the transformation using coordinate notation. A(1, 1) → A′( , ) B(3, 2) → B′( , ) C(4, –1) → C′( , ) D(2, –3) → D′( , )

Example 4B: Reflect a Figure in the x or y axis Graph quadrilateral ABCD and its image under a reflection in the y -axis. A(1, 1) → A′( , ) B(3, 2) → B′( , ) C(4, –1) → C′( , ) D(2, –3) → D′( , )

Guided Practice 4A: Reflect a Figure in the x or y axis Graph quadrilateral LMNO with vertices L(3, 1), M(5, 2), N(6, –1), and O(4, –3) and its reflected image in the x-axis. Select the correct coordinates for the new quadrilateral L'M'N'O'.

Guided Practice 4B: Reflect a Figure in the x or y axis Graph quadrilateral LMNO with vertices L(–1, 0), M(1, 1), N(2, –2), and O(0, –4) and its reflected image under the y-axis. Select the correct coordinates for the point M' in the new quadrilateral L'M'N'O'.

Geometry Unit 3 Rigid Transformations and Symmetry Note Sheets

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Example 5: Reflect a Figure in the line y = x Quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection of the line y = x.

Guided Practice 5: Reflect in the line y = x Quadrilateral EFGH has vertices E(–3, 1), F(–1, 3), G(1, 2), and H(–3, –1). Graph EFGH and its image under reflection of the line y = x. Select the correct coordinates for the point H' in the new quadrilateral E'F'G'H'.