Math Problem Statement

RSTU and VXYZ are quadrilaterals. Given RSTU ~ VXYZ, describe a sequence of rigid motions followed by a dilation with center (0,0) that maps RSTU to VXYZ.

Solution

To describe the transformation sequence that maps quadrilateral RSTU to VXYZ, let's analyze the situation based on the image provided.

  1. Reflection Across the Axes: Looking at the positions of quadrilaterals RSTU and VXYZ, we can identify that RSTU has been reflected across the y-axis, as its reflection results in a mirrored shape in the opposite direction.

  2. Translation: After reflection, the shape undergoes a translation, moving a certain number of units either up or down. By inspecting the graph, it appears that the translation has occurred downward by 4 units.

  3. Dilation: Lastly, there is a dilation with the center at (0, 0), which means the shape has been scaled by a certain factor. By looking at the size difference between RSTU and VXYZ, we can infer that the dilation involves a scale factor of 2, as the larger shape appears twice the size of the original.

So, the correct sequence is:

  • Reflection across the y-axis
  • Translation 4 units down
  • Dilation with center (0, 0) and scale factor 2

Thus, the correct answer is C.

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Math Problem Analysis

Mathematical Concepts

Transformations
Reflections
Translations
Dilations
Similarity

Formulas

Dilation formula: (x, y) -> (kx, ky)

Theorems

Properties of Similar Figures
Rigid Motion Theorem

Suitable Grade Level

Grades 8-10