Symmetry and Reflections

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