Reflections
- Author:
- Julianne Aviles
Constructing Reflections
A reflection is a transformation made where the image is equidistant to the pre-image and the line of reflection creates a perpendicular bisector. The line of reflection will form a 90 degree angle with any segment connecting any points on the pre-image with its image. This reflection is accurate, and doing it out without a graph would prove its accuracy. If you're given figure ABCD and this line to reflect it over, the presigure you would do starts with using you compass to construct a circle around the point A that has a radius large enough that it crosses line EF at two points. Label these points whatever you like, for example we'll use K and L. Next construct a circle around point K, make sure the circle has radius KA, the circle should have a radius just large enough that it intersects point A. Next repeat the previous step for point L. By now you should have three circles, circles K and L intersect somewhere below the line of reflection. This point is point A'. Repeat all of the above steps for the remaining points, points B, C, and D (before doing this I recommend erasing you previous work so that you only have point A', if you don't it will get a bit confusing on which lines belong to what). At this point you have four point points on the opposite side of the line of reflection than the pre-image, connect all the points to get figure A'B'C'D', or your reflection. This reflection will be just like on the graph above. This way you can see how the reflection above is accurate.