MA 08 transformations

2.3 Reflections

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Topic/Objectives

Reflection Identify and use reflections in a

plane. Understand Line Symmetry

Essential Question: How can you reflect over a line?

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ReflectionA reflection in line m is a transformation that maps every point P in the plane to point P’ so the following properties are true:

Line of Reflection

m

P P’

P and P’ are equidistant from line m.

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Reflections on the Coordinate Plane

Graph the reflection of A(2, 3) in the x-axis.

3

3

A’(2, -3)

A(2, 3) A’(2, -3)

A Reflection in the x-axis has the mapping:

(x, y) (x, -y)

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Reflections on the Coordinate Plane

Graph the reflection of A(2, 3) in the y-axis.22

A’(-2, 3)A(2, 3) A’(-2, 3)

A Reflection in the y-axis has the mapping:

(x, y) (-x, y)

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Reflections on the Coordinate Plane

Graph the reflection of A(1, 4) in the line y = x.

A’(4, 1)

A(1, 4) A’(4, 1)

A Reflection in the line y = x has the mapping:

(x, y) (y, x)

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Reflection Mappings In the x-axis: (x, y) (x, -y) In the y-axis: (x, y) (-x, y) In y = x: (x, y) (y, x)

We say: Reflect in the x-axis, reflect over the x-axis, reflect on the x-axis, reflect across the x-axis. They mean the same thing.

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Reflect RST in y-axis.

R

S

T

Determine coordinates.

Mapping Formula:

(x, y) (-x, y)

R(0, 4) R’(0, 4)

S(-4, 1) S’(4, 1)

T(-1, -2) T’(1, -2)

(0, 4)

(-4, 1)

(-1, -2)T’(1, -2)

S’(4, 1)

R’(0, 4)

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Reflect ABCD in the x-axis.

Mapping Formula:

(x, y) (x, -y)

A(-2, 2) A’(-2, -2)

B(-3, -1) B’(-3, 1)

C(3, -1) C’(3, 1)

D(2, 2) D’(2, -2)

A(-2, 2)

B(-3, -1) C(3, -1)

D(2, 2)

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Reflect AB on the line x = 2.

A(1, 3)

B(0, 1)

A’(3, 3)

B’(4, 1)