reflections geometry unit 7, lesson 1 mrs. king. brainpop! yandmeasurement/transformation/previ...

Reflections

GeometryUnit 7, Lesson 1Mrs. King

BrainPop!

http://www.brainpop.com/math/geometryandmeasurement/transformation/preview.weml

What is a Reflection?

Definition:A flip.

Example?

How to do a Reflection

1. Plot the point(s).

2. Count from the point to the line of reflection.

3. Count the same number of spaces in the opposite direction.

4. Plot the image.

Graphing Coordinates Plot the point A(4,6). Reflect the point

(4,6) over the x-axis. Label this point A’ and state the coordinates.

Reflect the point (4,6) over the y-axis. Label this point A” and state the coordinates.

y

x

10

10

-10

-10

A

A’

A”

(4,-6)

(-4,6)

Refresh Your Memory: Horizontal and Vertical Lines

Graph the following lines:– Y=5– Y=-2– X=4– X=-6

y

x

10

10

-10

-10

Y=5

Y=-2

X=4X=-6

Graphing Coordinates

Plot the point A(4,6).

Reflect the point (4,6) over the line x=-1. Label this point A’.

Reflect the point (4,6) over the line y=2. Label this point A”.

y

x

10

10

-10

-10

AA’

A”(-6,6)

x=-1

y=2

(4,-2)

More Reflection Examples

Graph the vertices of parallelogram WXYZ.– W(-3,5)– X(1,5)– Y(2,3)– Z(-2,3)

Reflect the parallelogram over the x-axis.

y

x

10

10

-10

-10

W X

YZ

W’X’

Y’Z’

W’(-3,-5)X’(1,-5)Y’(2,-3)Z’(-2,-3)

More Reflection Examples

Graph the vertices of parallelogram WXYZ.– W(-3,1)– X(1,1)– Y(2,-1)– Z(-2,-1)

Reflect the parallelogram over the line x=-2

y

x

10

10

-10

-10

W X

YZx=-2

W’X’

Y’ Z’

W’(-1,1)X’(-5,1)Y’(-6,-1)Z’(-2,-1)

Video Example

Practice with Line Reflections

http://www.regentsprep.org/Regents/math/geometry/GT1/Prac1.htm

More Practice:

The image of the point (4,-3) under a reflection across the x-axis is…

(4,3)

The image of the point (-5,4) under a reflection across the y-axis is…

(5,4)

Think about it:

The image of the point (-1, 8) under a reflection across the line y = x is …

(8, -1)