after today’s lesson you will be able to: use a mira/reflecta to: sketch the reflection of figure...

Objectives:After today’s lesson you will be able to:•use a Mira/Reflecta to:

•sketch the reflection of figure across a line of reflection•determine whether an image is a reflection of its pre-image

•identify the properties of a reflection•use the properties of a reflection to solve real-world problems

(Reed)

Review from Yesterday:•Transformation: a general term for four specific ways to

manipulate the shape of a point, a line, or figure.

These include: translations, reflections, rotations, and dilations

•Preimage: the figure prior to a transformation

•Image: the figure after the transformation •Isometry: a transformation that preserves congruence.

•Translations•Rotations•Reflections ("http://www.mathwarehouse.com/transformations/ ," )

Introduce Mira/Reflecta

("Mira," )

A Mira is a tool that has the reflective quality of a mirror, as well as a transparent quality to help us in transformational geometry.

Warm-ups:("Warm up," 2009)

Properties of a Reflection •Is an isometry – rigid transformation that preserves congruence.

•The image has the opposite orientation of its preimage

•The line of reflection is the perpendicular bisector of the line connecting every image point with its preimage (a point and its image are equidistant from the line of reflection).

(Allen, 2011)

Properties of Reflections Partner Activities

("what is trust," 2011)

A Real World Application of Reflection

We are going to learn exactly where we should hit the ball to get a hole-in-one in miniature golf every time!

But first we need to learn a little about physics….

An incident ray of light strikes a surface…

There is a line normal to the surface at the point of

Angle of Incidence The angle formed by an incident ray on a surface and a normal line to the surface at the point of incidence.

The ray that is reflected at the point of incidence is called the reflected ray.

Angle of Reflection The angle formed by a reflection ray on a surface and a normal line to the surface at the point of incidence.

Assuming that there is no spin on the ball….

( and the ball is rolling on a smooth surface and bounces off a smooth wall )

Law of Reflection

mini golf

The Geometer’s Sketchpad

Review•Today we learned how to use a Mira/Reflecta to reflect images across a mirror line.

•We discovered the properties of a reflection transformation. When an object is reflected, the image is congruent to the preimage, and the image’s orientation is reversed. All points on the image and the corresponding preimage points are equidistant to the line of reflection.

•We looked at some real-world applications for reflections

Referenceshttp://www.mathwarehouse.com/transformations/. (n.d.). Retrieved from Transformations in math

Maureen712. (Producer). ( 2009). Reflections - diana ross. [Web Video]. Retrieved from http://www.youtube.com/watch?v=qxoBzzDP5lU(n.d.). Mira. [Web Photo]. Retrieved from http://images.shopcpw.com/view/1/cpw/product-images/noimage.jpg/2/cpw/product-images/52195-0.jpg

Okerstrom,, J. (Designer). (2011). Retrieved from library.creativecow.net

Reed, M. (Designer). (n.d.). Retrieved from http://redwing.hutman.net/~mreed/Assets/target.jpg

(2009). Warm up. (2009). [Web Drawing]. Retrieved from http://teacherweb.com/NJ/EastBrunswickHS/EBBearCare

(2011). What is trust. (2011). [Print Photo]. Retrieved from http://jumpfoundation.files.wordpress.com/2010/11/reflections3.jpg