12.1.1 Reflections (continued) Example 4 Drawing Reflections in the Coordinate Plane
The reflection of a figure is drawn in the coordinate plane in this example. The coordinates of the vertices of the preimage figure and the line of reflection are given. To draw the reflection across the x -axis, count the distance to the x -axis in the y direction of each vertex of the preimage. Count the same distance below the x -axis to locate the image vertex. Draw lines joining the three image vertex points to construct the reflected triangle. It is also possible to apply the rule for the reflection, which is described as the transformation of the point ( x , y ) to ( x , − y ). So, for example, A (1, 3) is transformed in the reflection to A ′(1, − 3). The reflection of a figure is drawn in the coordinate plane in this example. The coordinates of the vertices of the preimage figure and the line of reflection are given. To find the image as it is reflected from the preimage across the x = y line, apply the transformation rule, ( x , y ) → ( y , x ), to each of the preimage points. For example, D (1, 3) → D ′(3, 1). Find each of the vertices of the image in this way and draw lines between them to construct the reflected figure.
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