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Do Now1) Draw a coordinate grid (like below) and label the axes2)Graph the point (2,1)3) Translate (2,1) 4 units up and 1 unit left4)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 ∆A’B’C’. 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-AXIS ORIGIN Y=X Right 2 units, down 3 units, AND reflected in the Y-AXIS
TriangleA(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. 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)
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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 (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)
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Homework
Reflections Worksheet