What is true about the image \( \triangle \mathrm{K}^{\prime} \mathrm{L}^{\prime} \mathrm{M}^{\prime} \) ? Select three options. \( \overline{\mathrm{KM}} \) is shorter than \( \overline{\mathrm{K}^{\prime} \mathrm{M}^{\prime}} \) The vertices of the image are closer to the origin than those of the pre-image. The distance from \( \mathrm{M}^{\prime} \) to the origin is exactly half the distance from M to the origin.

To solve this problem, we need to analyze the given information about the image \( \triangle \mathrm{K}^{\prime} \mathrm{L}^{\prime} \mathrm{M}^{\prime} \) and compare it with the pre-image \( \triangle \mathrm{KLM} \). Let's go through each statement and determine if it is true or false. 1. \( \overline{\mathrm{KM}} \) is shorter than \( \overline{\mathrm{K}^{\prime} \mathrm{M}^{\prime}} \) This statement is not necessarily true. Without additional information about the transformation that maps \( \triangle \mathrm{KLM} \) to \( \triangle \mathrm{K}^{\prime} \mathrm{L}^{\prime} \mathrm{M}^{\prime} \), we cannot determine the relative lengths of \( \overline{\mathrm{KM}} \) and \( \overline{\mathrm{K}^{\prime} \mathrm{M}^{\prime}} \). The transformation could be a scaling, rotation, reflection, or translation, and each of these would affect the lengths differently. 2. The vertices of the image are closer to the origin than those of the pre-image. This statement is not necessarily true. Again, without knowing the specific transformation, we cannot determine the relative distances of the vertices to the origin. The transformation could bring the vertices closer to the origin, or it could move them further away. 3. The distance from \( \mathrm{M}^{\prime} \) to the origin is exactly half the distance from M to the origin. This statement is true if the transformation is a dilation with a scale factor of 1/2. In a dilation, the image is a scaled-up or scaled-down version of the pre-image, and the scale factor determines how much larger or smaller the image is compared to the pre-image. If the scale factor is 1/2, then the distance from \( \mathrm{M}^{\prime} \) to the origin will be exactly half the distance from M to the origin. Therefore, the correct answer is: - The distance from \( \mathrm{M}^{\prime} \) to the origin is exactly half the distance from M to the origin.