Answer
The valid statements are 0.75 (x,y) = (0.75x, 0.75y), LM is parallel to L’M’, and “the vertices of the image are closer to the origin than those of the pre-image.” Explanation: The dilation of triangle ABC under the rule DO, 0.75 (x,y) means both x- and y-coordinates are scaled by 0.75, indicating a dilation about the origin with a scale factor of 0.75. Thus, the first statement holds true. With both coordinates being multiplied by 0.75, the image’s sides are parallel to those of the pre-image, making the second statement “LM is parallel to L’M'” accurate. However, the third and fifth statements are incorrect. Since the scale factor is less than 1, the image’s vertices indeed lie closer to the origin compared to the pre-image, validating the fourth statement “the vertices of the image are closer to the origin than those of the pre-image.”
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