Overview: What Are Reflecting Points?
Reflecting points and images in geometry are a special type of transformation. Every point in the preimage corresponds exactly to every point in the reflected image. If a line separates the preimage and the reflected image, every point in the preimage and the reflected image will be connected by a perpendicular line.
Line of Reflection
The line between the preimage and reflected image is called a line of reflection. It depends on the location of the preimage and reflected image, so it does not have to be horizontal or vertical. If the preimage consists of just a few points, the reflected image can be constructed using a protractor and measuring the angles between those points on either side of the line of reflection.
Reflecting Figures
Whether figures are simple or complex, reflections have several features in common. An angle <AEH and its reflected image <A’E’H’ will have all distances, angles, and collinear points in exactly the same relationship in both figures. This is called the ABCD relationship between preimages and their reflected images, because angle measure, betweenness, collinearity, and distance measurement are all preserved.
Shortcuts to Reflecting Figures
Most figures in geometry are not simple sets of points, but infinite numbers of points. In order to draw a reflected image from a preimage, shortcuts are often necessary. A line contains an infinite number or points, as does its reflected image. Therefore, a line segment and its reflected image will preserve collinearity, betweenness and distance measurement. A more complex preimage and its reflected image can be drawn by tracing or by using a mirror.
Computer Drawing Programs
Computer programs make use of mathematical algorithms to construct any figure. Therefore, the relationships between the points in preimages and their reflected images can be used in equations. The angle measures, betweenness, collinearity, and distance measurement will be the same in the preimage and its reflected image.
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