Question

9 multiple choice 1 point which is a true statement about dilations? a dilation sometimes enlarges a figure. a dilation always changes the orientation of a figure. a dilation sometimes changes the orientation of the vertices. a dilation always preserves congruence. clear my selection

Explanation:

• Option A: A dilation can have a scale factor \(k> 1\) (enlarges the figure), \(0 < k<1\) (reduces the figure), or \(k = 1\) (the figure remains the same size). So, a dilation sometimes enlarges a figure.
• Option B: A dilation is a similarity transformation that does not change the orientation of a figure. For example, if you dilate a triangle with vertices \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\) about a center of dilation \((a,b)\) with a scale factor \(k\), the order of the vertices (e.g., clock - wise or counter - clockwise) remains the same.
• Option C: As mentioned in the explanation for option B, a dilation does not change the orientation of the vertices. The relative positions of the vertices with respect to each other (in terms of clock - wise or counter - clockwise order) are preserved.
• Option D: A dilation changes the size of a figure (unless \(k = 1\)). Congruent figures have the same size and shape. If \(k

eq1\), the pre - image and the image are similar (same shape, different size), not congruent.

Answer:

A. A dilation sometimes enlarges a figure.