Symmetry and Reflections

Objectives

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

Vocabulary

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

the two halves match like a mirror image the

figure has line symmetry. - A reflection is a movement that flips an entire

figure over a line called a line of reflection.

Real-World Symmetry Connection

- Line symmetry can be found in works of art and in

nature. - Some figures, like this tree, Others, like

this snowflake, - have only one line of symmetry. have multiple

lines of symmetry.

Vertical, horizontal, diagonal symmetry

Vertical symmetry

Paper Practice

- Using your ruler, draw all lines of symmetry for

each figure. - When you finish, check your results with your

partner. - Expand your mind how many lines of symmetry does

a circle have?

Reflections

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

toward the mirror? away from the mirror? - When a figure is reflected, the image is

congruent to the original. - The actual figure and its image appear the same

distance from the line of reflection, here the

mirror.

Discovery Learning

- Use GeoGebra to explore how a point is reflected

over the y-axis on the coordinate plane. - Try moving point A on both sides of the y-axis.
- In your notebook, list 3 positions of A and its

corresponding reflection at A. - Summarize your findings.
- When finished, discuss with your neighbor.
- Follow the above steps to reflect a point over

the x-axis. - What is similar/different about your findings?

Reflecting a Point

- We learned how to graph a point as an ordered

pair on the coordinate plane. - The point A(1, -2) is in quadrant IV.

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

y-axis

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!

Similarly, to graph the reflection of a point

over the x-axis, simply change the sign of the

y-coordinate!

Reflecting a Figure

- Use these same steps to reflect an entire figure

on the coordinate plane - Identify which axis is the line of symmetry (the

mirror). - Individually reflect each endpoint of the figure.
- Connect the reflected points.
- Lets try on paper! (Practice 10-7)