Final answer:
Dilation changes the size of the figure and preserves angles but not distances. Translation and reflection maintain both the distance and angle of a figure. Therefore, the dilation of the quadrilateral preserves only angles, while the translation and reflection of the rhombus, as well as the translation and dilation of the triangle, preserve both distances and angles.
Step-by-step explanation:
Types of Geometric Transformations
There are several geometric transformations that can be applied to figures on the coordinate plane, each affecting the figure's properties like distances and angles in different ways.
Dilation is a transformation that changes the size of the figure while keeping its shape. When a quadrilateral is dilated by a scale factor of 2, all distances between corresponding points on the original figure and the image are multiplied by 2. This means that the dilated figure preserves angles but not the actual distances.
Translation is a type of transformation that slides a figure without changing its shape or size. Translating a rhombus 3 units to the right will move the figure, maintaining both distance and angle. Similarly, a reflection across an axis is another transformation that flips a figure over a line. Reflecting a translated rhombus across the x-axis will also preserve both distance and angle as the shape and size of the rhombus remain constant.
The combination of translation and dilation, as in the case of translating a triangle 2 units to the left and then performing a dilation by a scale factor of 0.5, results in changes to distances but preservation of angles. The triangle's overall size is changed, but the angles remain the same due to the nature of dilation.
In summary, a dilation by a scale factor not equal to 1 will preserve angles but alter distances, while transformations such as translation and reflection maintain both distance and angle.