Symmetry and Reflections

ObjectivesObjectives Describe and identify lines of symmetry.Describe and identify lines of symmetry. Create reflections on a coordinate plane.Create reflections on a coordinate plane.

VocabularyVocabulary If a line can be drawn through a figure so that If a line can be drawn through a figure so that

the two halves match like a mirror image the the two halves match like a mirror image the figure has figure has line symmetryline symmetry. .

A A reflectionreflection is a movement that flips an entire is a movement that flips an entire figure over a line called a figure over a line called a line of reflectionline of reflection..

Real-World Symmetry ConnectionReal-World Symmetry Connection Line symmetry can be found in works of art and Line symmetry can be found in works of art and

in nature.in nature.

Some figures, like this tree, Some figures, like this tree, Others, like this snowflake, Others, like this snowflake,

have only one line of symmetry.have only one line of symmetry. have multiple lines of symmetry. have multiple lines of symmetry.

Vertical symmetry Vertical, horizontal, & diagonal symmetry

Paper PracticePaper Practice

Using your ruler, draw Using your ruler, draw allall lines of symmetry lines of symmetry for each figure.for each figure.

When you finish, When you finish, check your results check your results with your partner.with your partner.

Expand your mind: Expand your mind: how many lines of how many lines of symmetry does a symmetry does a circle have?circle have?

ReflectionsReflections

Look at yourself in a mirror!Look at yourself in a mirror! How does your reflection respond as you step How does your reflection respond as you step

toward the mirror? away from the mirror?toward the mirror? away from the mirror?

When a figure is reflected, the image is When a figure is reflected, the image is congruent to the original.congruent to the original.

The actual figure and its image appear the The actual figure and its image appear the same distance from the line of reflection, same distance from the line of reflection, here the mirror. here the mirror.

Discovery LearningDiscovery Learning

Use GeoGebra to explore how a point is reflected over Use GeoGebra to explore how a point is reflected over the y-axis on the coordinate plane.the y-axis on the coordinate plane. Try moving point A on both sides of the y-axis.Try moving point A on both sides of the y-axis. In your notebook, list 3 positions of A and its In your notebook, list 3 positions of A and its

corresponding reflection at A’.corresponding reflection at A’. Summarize your findings.Summarize your findings. When finished, discuss with your neighbor. When finished, discuss with your neighbor.

Follow the above steps to reflect a point over the x-axis. Follow the above steps to reflect a point over the x-axis. What is similar/different about your findings?What is similar/different about your findings?

Reflecting a PointReflecting a Point

We learned how to We learned how to graph a point as an graph a point as an ordered pair on the ordered pair on the coordinate plane.coordinate plane.

The point A(1, -2) is in The point A(1, -2) is in quadrant IV.quadrant IV.

1.Identify the y-axis as the line of symmetry (the mirror).

2. Point A is 1 unit to the right of the y-axis, so its reflection A’ is 1 unit to the left of the y-axis.

We discovered an interesting phenomenon: simply change the sign of the x-coordinate to reflect a point over the y-axis!

To graph the reflection of point A(1,-2) over the y-axis:To graph the reflection of point A(1,-2) over the y-axis:

Similarly, to graph the reflection of a point over the x-axis, simply change the sign of the y-coordinate!

Reflecting a FigureReflecting a Figure

Use these same steps to reflect an entire Use these same steps to reflect an entire figure on the coordinate plane:figure on the coordinate plane: Identify which axis is the line of symmetry (the Identify which axis is the line of symmetry (the

mirror).mirror). Individually reflect each endpoint of the figure.Individually reflect each endpoint of the figure. Connect the reflected points.Connect the reflected points.

Let’s try on paper! (Practice 10-7)Let’s try on paper! (Practice 10-7)