# Honors Geometry Companion Book, Volume 1

1.2.3 Transformations in the Coordinate Plane (continued)

In this example, the translation is defined by the rule ( x , y ) → ( x − 3, y + 2). This rule means that each preimage point ( x , y ) is translated 3 units left and 2 units up to get the corresponding image point. The translation rule does not need to be applied to every single point on the figure. Translating the figure’s vertices is sufficient. So, begin by identifying the coordinates of each vertex. Then apply the translation to the coordinates of each point. Specifically, subtract 3 from each x -coordinate and add 2 to each y -coordinate. Once the translation has been applied to all three of the preimage’s vertices, plot the three image points and connect the points with lines to draw the image. In this example the preimage and image of a translation are given and the translation rule must be written. To identify the rule, determine the distance and direction that a preimage point is moved. First, identify a point on the preimage and its image. Here, point A ( − 1, 1) on the preimage is mapped to A ′(1, − 1) on the image. A is translated 2 units to the right and 2 units down. In terms of the coordinates, “2 units to the right” means to add 2 to the x -coordinate and “2 units down” means to subtract 2 from the y -coordinate. So, the translation rule is ( x , y ) → ( x + 2, y − 2).

Example 4 Art History Application

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