Symmetry on the Rectangular Coordinate System

An Investigation


Procedures

Symmetry on the Rectangular Coordinate System: An Investigation

Start up the Sketchpad

Sketch:

  1. Open a new sketch.

  2. Go to Display menu, down to Preferences and Select Autoshow label for points.

  3. Go to Graph menu and click Create axes.

  4. Construct a triangle in the second quadrant. Construct the polygon interior of the triangle and color it. Shift —select the three vertices of the triangle by pressing the shift key and clicking the mouse simultaneously. Go to Construct, select polygon interior, go to Display and Color.

  5. Shift-select the vertices of the triangle, go to Measure and click Coordinates.

  6. Drag the coordinates and put them in the third quadrant.


Symmetry about the y-axis

  1. Select the y-axis as the mirror by selecting the y-axis, then go to Transform menu and click Mark Mirror.

  2. Select the whole triangle, go to Transform and choose Reflect.

  3. Using the new triangle, repeat step 5.

  4. Compare the coordinates of the original triangle and the reflection.

  5. Drag a vertex of a triangle and observe the behavior of the coordinates.

  6. Using the text tool, write your observations and conjectures on the Sketchpad about the reflection of points about the y-axis.


Symmetry about the x-axis

  1. Open a new sketch, go to Graph and Create axes.

  2. Construct a triangle in the first quadrant, Construct the polygon interior and color it, then find the coordinates of the vertices of the triangle.

  3. Mark the x-axis as the mirror, click on the x-axis and then repeat steps 8 thru 11.

  4. Using the text tool, write your observations and conjectures on the Sketchpad about the reflection of points about the x-axis


Symmetry about the line y=x

  1. Open a new sketch, go to Graph and Create axes.

  2. Construct a triangle in the second quadrant, construct its polygon interior and color it, then find the coordinates of the vertices of the triangle.

  3. Go to Graph and choose Plot Points. Plot the points, x=1, y=1; x=2, y=2 and x=3, y=3.

  4. Change Segment tool to Line, Go to Construct and click Line.

  5. Go to Measure, click Equation, and drag equation next to the line.

  6. Mark the line y=x as Mirror, select the line y=x and then repeat steps 8 thru 11.

  7. Using the text tool, write your observations and conjectures on the Sketchpad about the reflection of points about the line y = x.

Copy and Paste all three sketches on to a word processing program before printing.


The Integrating Technology into Math Instruction webpages project is partially funded by a grant from The Boeing Company. Integrating Technology into Math Instruction is a project of +PLUS+ and is displayed on the Los Angeles Educational Partnership Learning Exchange. +PLUS+ is an initiative of the Los Angeles Educational Partnership.
Updated June 2000