Example 2 Drawing Reflections 12.1.1 Reflections (continued)
The reflection of a figure is drawn in this example. The preimage and the line of reflection are given. To draw the reflected image, draw lines that are perpendicular to the line of reflection from the vertices of the preimage figure. Measure the distance from the vertex of the preimage to the line of reflection and then measure the same distance on the other side of the line of reflection. Mark the point for the vertex of the image. When all the vertices are transformed across the line of reflection, connect the vertices with line segments to draw the image figure.
Example 3 Landscape Architecture Application
A reflection is used to construct lines representing the shortest path from one point to a line and then a second point in this application example. To find this line, recognize that the shortest distance between two points is a straight line. However, the path between the points A and B must touch the river, so the shortest path will be the one that joins the reflection of one point with the other point through the line for the river (which is a straight line). To construct the line, find the reflection of B by drawing a line perpendicular to the river. Extend the line past the river the same distance between B and the river. Draw a line between B ′ and A . Draw a line that extends from the intersection of AB ′, point X , with the river line back to B . Since AX + XB = AX + XB ′, and the shortest distance between A and B ′ is a straight line, the solution shown is also the shortest distance between A and B that includes contact with the river.
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