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.

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Presentation transcript:

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

Review Homework Questions?

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

What is a reflection?

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

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

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

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

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

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

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

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

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

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

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)

Right 2 units, down 3 units, AND reflected in the Y-AXIS REFLECTIONS X-AXIS ORIGIN Y=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)  ( ) (x, y)  ( )

1. A’B’C’ 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)

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)]

Point R(a, b) is a vertex of quadrilateral QRST 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)

The point A(-1, 3) is transformed according to the rule (x’y’) = (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)

Homework Reflections Worksheet