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Main Idea/Vocabulary translation Graph translations on a coordinate plane.

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Example 1 Draw a Translation Copy ΔEFG below on graph paper. Then draw the image of the figure after a translation of 3 units right and 2 units up. Step 1Move each vertex of the triangle 3 units right and 2 units up. Answer: Step 2Connect the new vertices to form the image.

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1.A 2.B 3.C 4.D Example 1 Draw the image of ΔABC after a translation of 2 units right and 4 units down. A.B. C.D.

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1.A 2.B 3.C 4.D Example 1 Draw the image of ΔABC after a translation of 2 units right and 4 units down. A.B. C.D.

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Example 2 Translation in the Coordinate Plane Graph ΔABC with vertices A(–2, 2), B(3, 4), and C(4, 1). Then graph the image of ΔABC after a translation of 2 units left and 5 units down. Write the coordinates of its vertices.

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Example 2 Translation in the Coordinate Plane The coordinates of the vertices of the image are A'(–4, –3), B'(1, –1), and C'(2, –4). Notice that these vertices can also be found by adding –2 to the x-coordinates and –5 to the y-coordinates, or (–2, –5).

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Example 2 Translation in the Coordinate Plane OriginalAdd (–2, –5).Image A(–2, 2)(–2 + (–2), 2 + (–5))(–4, –3) B(3, 4)(3 + (–2), 4 + (–5))(1, –1) C(4, 1)(4 + (–2), 1 + (–5))(2, –4) Answer: A'(–4, –3), B'(1, –1), and C'(2, –4)

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1.A 2.B 3.C 4.D Example 2 Graph ΔPQR with vertices P(–1, 3), Q(2, 4), and R(3, 2). Then graph the image of ΔPQR after a translation of 2 units right and 3 units down. Write the coordinates of its vertices. A.P'(–1, 0), Q'(–4, 1), and R'(–5, 1) B.P'(1, 0), Q'(4, 1), and R'(5, –1) C.P'(–1, 0), Q'(–4, –1), and R'(–5, –1) D.P'(1, 0), Q'(4, –1), and R'(–5, –1)

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Example 3 A. (0, 3)B. (1, 2) C. (2, 1)D. (1, 1) If triangle RST is translated 4 units to the right and 3 units up, what are the coordinates of point T' ?

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Example 3 Read the Item You are asked to find the coordinates of point T' after the original figure has been translated 4 units right and 3 units up. Solve the Item You can answer this question without translating the entire triangle.

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Example 3 Original figure The coordinates of T' are (1, 2). Answer: The answer is B. Translating 3 units up is the same as adding 3 to the y-coordinate. Translating 4 units right is the same as adding 4 to the x-coordinate. The coordinates of point T are (–3, –1). The x-coordinate of T is –3, so the x-coordinate of T' is –3 + 4 or 1. The y-coordinate of T is –1, so the y-coordinate of T' is –1 + 3 or 2.

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1.A 2.B 3.C 4.D Example 3 A.(0, –1)B.(–3, 2) C.(–1, –4)D.(–2, 3) If triangle LMN is translated 4 units left and 2 units up, what are the coordinates of point L'?

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1.A 2.B 3.C 4.D Example 3 A.(0, –1)B.(–3, 2) C.(–1, –4)D.(–2, 3) If triangle LMN is translated 4 units left and 2 units up, what are the coordinates of point L'?

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1.A 2.B 3.C 4.D Five Minute Check 1 A.x-axis B.y-axis C.y = x D.y = –x Name the line of reflection for the pair of figures in the picture. (over Lesson 6-6)

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1.A 2.B 3.C 4.D Five Minute Check 1 A.x-axis B.y-axis C.y = x D.y = –x Name the line of reflection for the pair of figures in the picture. (over Lesson 6-6)

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1.A 2.B 3.C 4.D Five Minute Check 2 A.x-axis B.y-axis C.y = x D.y = –x Name the line of reflection for the pair of figures in the picture. (over Lesson 6-6)

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1.A 2.B 3.C 4.D Five Minute Check 2 A.x-axis B.y-axis C.y = x D.y = –x Name the line of reflection for the pair of figures in the picture. (over Lesson 6-6)

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1.A 2.B 3.C 4.D Five Minute Check 3 A.Q'(1, 1), R'(4, –3), S'(–2, –3) B.Q'(–1, 1), R'(4, –3), S'(–2, 3) C.Q'(1, –1), R'(4, –3), S'(–2, –3) D.Q'(–1, –1), R'(4, –3), S'(2, –3) Find the coordinates of the vertices of ΔQRS with vertices Q(1, 1), R(4, 3), and S(–2, 3) after a reflection over the x-axis. (over Lesson 6-6)

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1.A 2.B 3.C 4.D Five Minute Check 3 A.Q'(1, 1), R'(4, –3), S'(–2, –3) B.Q'(–1, 1), R'(4, –3), S'(–2, 3) C.Q'(1, –1), R'(4, –3), S'(–2, –3) D.Q'(–1, –1), R'(4, –3), S'(2, –3) Find the coordinates of the vertices of ΔQRS with vertices Q(1, 1), R(4, 3), and S(–2, 3) after a reflection over the x-axis. (over Lesson 6-6)

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1.A 2.B 3.C 4.D Five Minute Check 4 A.Square WXYZ was reflected over the x-axis. B.Square WXYZ was reflected over the y-axis. C.Square WXYZ was reflected over the line y = x. D.Square WXYZ was reflected over the line y = –x. Square WXYZ has vertices W(1, 2), X(1, 4), Y(3, 4), and Z(3, 2). If W'X'Y'Z' has vertices W'(–1, 2), X'(–1, 4), Y'(–3, 4), and Z'(–3, 2), describe the reflection performed on square WXYZ. (over Lesson 6-6)

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1.A 2.B 3.C 4.D Five Minute Check 4 A.Square WXYZ was reflected over the x-axis. B.Square WXYZ was reflected over the y-axis. C.Square WXYZ was reflected over the line y = x. D.Square WXYZ was reflected over the line y = –x. Square WXYZ has vertices W(1, 2), X(1, 4), Y(3, 4), and Z(3, 2). If W'X'Y'Z' has vertices W'(–1, 2), X'(–1, 4), Y'(–3, 4), and Z'(–3, 2), describe the reflection performed on square WXYZ. (over Lesson 6-6)

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