Advanced reflections

The  exercise appears under the 8th grade (U.S.) Math Mission and Geometry Math Mission. This exercise practices reflection on the coordinate plane over lines of arbitrary slope.

Types of Problems
There is one type of problem in this exercise:


 * 1) Make the reflection over the line: This problem provides a figure and a reflecting line. The student is expected to create the image after the figure is reflected over the line. The lines on this exercise can have any slope.Reflections2-1.png

Strategies
Knowledge of the coordinate plane and geometric transformations, particularly reflections, are encouraged to ensure success on this exercise.
 * 1) The reflections on this exercise are over possibly slanted lines. Since there are points that need to be on lattice points, finding a "cross" or "T" pattern can help to connect an image point to the pre-image point (especially at endpoints).
 * 2) A reflection line is needed to define the reflection, and two points determine a line.
 * 3) By connecting the endpoints of the images and preimages you can find lines perpendicular to the line of reflection.

Real-life Applications

 * 1) Reflection is a size preserving transformation, so figures are kept congruent, but it reverses orientation.
 * 2) Reflections connect with perpendicularity and mirror reflection.
 * 3) Art, modern and classic, have connections with all geometric transformations.
 * 4) Architecture, drafting and engineering make use of geometric transformations.