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Lesson Menu Five-Minute Check (over Lesson 2–6) Then/Now New Vocabulary Key Concept: Translations and Reflections Example 1: Standardized Test Example Example 2: Reflections on a Coordinate Plane

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Over Lesson 2–6 5-Minute Check 1 A.(6, 4) B.(–6, 4) C.(6, –4) D.(–6,–4) Name the ordered pair for point D.

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Over Lesson 2–6 5-Minute Check 2 A.(9, 4) B.(–9, 4) C.(9, –4) D.(–9, –4) Name the ordered pair for point G.

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Over Lesson 2–6 5-Minute Check 3 A.(5, 0) B.(0, 5) C.(–5, 0) D.(0 –5) Name the ordered pair for point E.

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Over Lesson 2–6 5-Minute Check 4 A.point F; quadrant IV B.point F; quadrant III C.point F; quadrant II D.point G; quadrant III Name the point located at (–3, –3). Then name the quadrant in which the point lies.

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Over Lesson 2–6 5-Minute Check 5 A.point C; quadrant I B.point C; quadrant II C.point A; quadrant I D.point A; quadrant II Name the point located at (8, 2). Then name the quadrant in which the point lies.

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Over Lesson 2–6 5-Minute Check 5 A.(positive, positive) B.(negative, negative) C.(positive, negative) D.(negative, positive) What are the signs of the x- and y-coordinates of a point located in quadrant IV?

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Then/Now You have already graphed points on a coordinate plane. (Lesson 2–6) Define and identify transformations. Draw translations and reflections on a coordinate plane.

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Vocabulary Transformation – A movement of a geometric figure. Image – Every corresponding point on a figure after its transformation. Translation – A transformation where a figure is slid from one position to another without being turned. Slide. Reflection – A transformation where a figure is flipped over a line. Flip. Line of symmetry – Each half of a figure is mirror image of the other half when a line of symmetry is drawn.

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Concept

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Example 1 Triangle ABC is shown on the coordinate plane. Find the coordinates of the vertices of the image if the triangle is translated 4 units right and 5 units down. AA'(–7, 2), B'(–5, –5), C'(1, 0) BA'(1, 12), B'(3, 5), C'(9, 10) CA'(–7, 12), B'(–5, 5), C'(1, 10) DA'(1, 2), B'(3, –5), C'(9, 0)

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Example 1 Read the Test Item This translation can be written as the ordered pair (4, –5). To find the coordinates of the translated image, add 4 to each x-coordinate and add –5 to each y-coordinate. Solve the Test Item Answer: The answer is D. originaltranslationimage A(–3, 7)+(4, –5) A'(1, 2) B(–1, 0)+(4, –5) B'(3, –5) C(5, 5)+(4, –5) C'(9, 0)

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Example 1 A.A'(1, 2), B'(–3, –2), C'(0, –3) B.A'(3, 2), B'(–1, –2), C'(2, –3) C.A'(1, 8), B'(–3, –4), C'(0, 3) D.A'(3, 8), B'(–1, –4), C'(2, 3) A triangle has vertices at A(2, 5), B(–2, 1) and C(1, 0). What are the coordinates of the vertices if the triangle is translated 1 unit left and 3 units down?

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Example 2 Reflections on a Coordinate Plane The vertices of figure MNOP are M(–8, 6), N(5, 9), O(2, 1), and P(–10, 3). Graph the figure and the image of the figure after a reflection over the y-axis. To find the coordinates of the vertices of the image after a reflection over the y-axis, multiply the x-coordinate by –1 and use the same y-coordinate. M(–8, 6) M'(8, 6) N(5, 9) N'(–5, 9) O(2, 1) O'(–2, 1) P(–10, 3) P'(10, 3) same opposite

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Example 2 Answer: Reflections on a Coordinate Plane

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Example 2 A.A'(2, 1), B'(–2, –3), C'(–3, 0) B.A'(1, –2), B'(–3, 2), C'(2, –3) C.A'(–1, –2), B'(–3, –2), C'(0, 3) D.A'(–1, 2), B'(–3, –2), C'(0, –3) A triangle has vertices at A(1, 2), B(3, –2) and C(0, –3). What are the coordinates of the vertices if the triangle is reflected over the y-axis?

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End of the Lesson

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