do now 1) draw a coordinate grid (like below) and label the axes 2)graph the point (2,1) 3)...

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

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.

A

B

C

A’

B’

C’

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

b) Reflected across the y-axis(x, y) (___________)New coordinates: ( )

(-1, 2)Verbal to algebraic

c) Reflected over the origin(x, y) (___________)New coordinates: ( )

(-1, 2)Verbal to algebraic

d) Reflected over the line y = x(x, y) (___________)New coordinates: ( )

(-1, 2)Verbal to algebraic

•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

a) (x, y) (-x, y)_______________________New coordinates: ( )

(2, 1)Algebraic to Verbal

(2, 1)Algebraic to Verbal

b) (x, y) (-x, -y)______________________New coordinates: ( )

(2, 1)Algebraic to Verbal

c) (x, y) (y, x)_______________________New coordinates: ( )

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)

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: ( , )( , )( , ) 

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. 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