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Do Now 1) Draw a coordinate grid (like below) and label the axes 2)Graph the point (2,1) 3) Translate (2,1) 4 units up and 1 unit left 4)Write the translation algebraically

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Review Homework Questions?

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Reflections Objective: Describe reflections in the coordinate plane in algebraic terms, find new coordinates of translated polygons, and graph the reflections.

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What is a reflection?

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ABC underwent a change and became ABC. Describe the change. A B C A B C

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Reflection A reflection flips a figure over a line. y x

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(-1, 2) a) reflected over the x axis (x, y) (___________) New coordinates: () Verbal to algebraic

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b) Reflected across the y-axis (x, y) (___________) New coordinates: () (-1, 2) Verbal to algebraic

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c) Reflected over the origin (x, y) (___________) New coordinates: () (-1, 2) Verbal to algebraic

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d) Reflected over the line y = x (x, y) (___________) New coordinates: () (-1, 2) Verbal to algebraic

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e) Translated 3 units down and 1 unit left, then reflected over the line y = x (x, y) (___________) New coordinates: ( ) (-1, 2) Verbal to algebraic

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a) (x, y) (-x, y) _______________________ New coordinates: () (2, 1) Algebraic to Verbal

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(2, 1) Algebraic to Verbal b) (x, y) (-x, -y) ______________________ New coordinates: ()

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(2, 1) Algebraic to Verbal c) (x, y) (y, x) _______________________ New coordinates: ()

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Special Reflections Reflection across x – axis: Reflection across y – axis: Reflection over origin: Reflection over line y = x: (x, y ) (x, -y) (x, y ) (-x, y) (x, y ) (-x, -y) (x, y ) (y, x)

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REFLECTIONS X-AXISORIGINY=X Right 2 units, down 3 units, AND reflected in the Y-AXIS Triangle A(6, 4) B(2, 7) C(8, 12) ( x, y) ( ) New Points: (, ) (x, y) ( ) New Points: (, ) (x, y) ( ) New Points: (, ) (x, y) ( ) New Points: (, )

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1. ABC is the image produced after reflecting ABC over the line y = x. If vertex B has coordinates (s, t), what are the coordinates of B ? A(s, -t) B(t, s) C(-s, t) D(-s, -t)

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What is the rule for the transformation formed by a translation one unit to the left and two units up followed by a reflection over the y-axis? A(x – 1, y + 2) B[-(x – 1), y + 2] C[-(x – 1), -(y – 4)] D[x – 4, -(y – 1)]

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Point R(a, b) is a vertex of quadrilateral QRST. What are the coordinates of R after QRST is reflected over the x-axis? A(b, a) B(-a, b) C (-a, -b) D(a, -b)

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The point A(-1, 3) is transformed according to the rule (xy) = (x – 2, y + 1). The image of A is then reflected over the origin, resulting in point A. What are the coordinates of A? A(-3, 4) B(3, -4) C(4, -3) D(-3, -4)

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Homework Reflections Worksheet

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