Question

the figure that results from a transformation, such as a translation, is called the image. the original figure is called the preimage. a translation is the movement of a figure along a straight line. aran says that if the pawn shown below is translated 2 inches right, the preimage and the image will have the same parallel line segments and will be the same height and width. hiro says the parallel line segments will remain parallel but the height and width will not be the same. who is correct? a. fill in the dimensions and angle measures. are the dashed segments parallel? b. trace the pawn. translate your tracing 2 inches right. what is the relationship between the dimensions, angle measures, and parallel segments of the preimage and image? c. which student is correct? d. what translation must aran perform on the image so that it returns to the exact location of the preimage? turn and talk does the direction or distance a figure is translated affect the side lengths, relationships between sides, or angle measures of the figure? explain.

Explanation:

Part A

Step1: Recall Translation Properties

Translation is a rigid transformation, so preimage and image are congruent. Congruent figures have equal dimensions, equal angle measures, and parallel segments remain parallel.

Step2: Analyze Dashed Segments

Since translation preserves parallelism, the dashed segments (corresponding in preimage and image) are parallel. Dimensions (height, width) and angle measures are equal.

Step1: Perform Translation

Trace the pawn, move the tracing 2 inches right (translation).

Step2: Compare Preimage and Image

In translation (rigid transformation), corresponding dimensions (height, width) are equal, corresponding angle measures are equal, and parallel line segments remain parallel.

Step1: Recall Translation Effects

Translation is a rigid transformation, so preimage and image are congruent (same size, shape, parallel segments).

Step2: Evaluate Aran and Hiro

Aran says parallel segments remain and height/width same (correct, as congruent). Hiro says height/width not same (incorrect, since translation preserves size).

Answer:

The dashed segments are parallel. Dimensions (height, width) and angle measures of preimage and image are equal.

Part B