To determine which statement about figures X and Y is true, we need to analyze the types of transformations involved: translations and dilations, and whether they result in congruent figures.
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Translation: This transformation slides a figure from one position to another without changing its shape or size. If figure X can be transformed into figure Y through a series of translations, they will be congruent.
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Dilation: This transformation changes the size of a figure but keeps its shape the same. If figure X can be dilated to become figure Y, then they will not be congruent unless the dilation factor is 1 (which means no change in size).
Given these definitions, we can evaluate the statements:
A. A series of translations will transform figure X to figure Y, but the figures will not be congruent.
- This is false because translations do not change congruence.
B. A dilation will transform figure X to figure Y, but the figures will not be congruent.
- This is true if the figures are not the same size after the dilation.
C. A dilation will transform figure X to figure Y, and the figures will be congruent.
- This is false unless the dilation factor is 1.
D. A series of translations will transform figure X to figure Y, and the figures will be congruent.
- This is true only if they can be moved to coincide without changing size or shape.
Without the visual reference of figures X and Y, we can't definitively conclude which statement is correct. However, you would select the statement that reflects whether they have undergone size changes (dilation) or only changes in position (translation).
If the figures are of the same size and shape, D would be true. If they are different sizes but similar in shape, then B may be true. If you could clarify whether they are the same size or shape, it would help narrow it down.