# Mathematical Reflections

This applet investigates mathematical reflections, and is one in series on transformation of shapes. Learn how to draw reflections, and find the line of reflection (mirror, bilateral) symmetry using a perpendicular bisector.

###### Author and programmer: Ron Barrow

UK Years 7-11, KS3, KS4, Higher and Foundation GCSE Mathematics - Geometry, Shape and Space

## How to Use this Applet

At the start you will see a shape in the centre (the object) and the same shape in a different colour (the image) some distance away from it. The image is a reflection of the object, in the line y = x. At any time you can:
• change the shape of the object by clicking and dragging its red dots. This will change the image as well.
• change the line of reflection by clicking and dragging its red dots. This will change the image while the object stays still.
• show or hide the line of reflection by ticking or unticking the "Line" box.
• show or hide the equation of the line of reflection, if it is visible, by ticking or unticking the "Equation" box.
• turn on or off a connecting line (ray) by ticking or unticking its box ("Ray").
• turn on or off the Perpendicular Bisector of the ray by ticking or unticking its box ("Perp. Bisector") - I'll leave you to discover why!
• turn on or off the axes or the gridlines by ticking or unticking the "Axes" or "Gridlines" boxes.
• decide whether you want filled solid shapes or empty outlines by ticking or unticking the "Shapes filled" button.
• return to the start position by clicking the "Reset" button at the top of the screen.
There is a great deal of investigation to be done using this applet. Play around. Enjoy yourself as you learn.