Question

figure w and figure y are shown on the coordinate grid. figure y is a transformation of figure w. which pair of statements describes the transformations that were used to create figure y and explains why it is not congruent to figure w? a a reflection and a rotation create figure y. figures w and y are not congruent because rotations do not preserve size. b a reflection and a rotation create figure y. figures w and y are not congruent because reflections do not preserve orientation. c a reflection and a dilation create figure y. figures w and y are not congruent because dilations do not preserve size. d a reflection and a translation create figure y. figures w and y are not congruent because translations do not preserve orientation.

Explanation:

• Reflection: A reflection flips a figure over a line.
• Rotation: A rotation turns a figure around a point.
• Dilation: A dilation resizes a figure.
• Translation: A translation slides a figure without resizing or rotating.
• Congruent figures have the same shape and size.
• Reflections and rotations preserve size and shape (congruence), but dilations change size (so figures are not congruent if dilation is involved).

Answer:

C. A reflection and a dilation create figure Y. Figures W and Y are not congruent because dilations do not preserve size.