Question

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the figure that results from a transformation is called the image. figure abcd is translated to get its image, figure efgh. look at \\( \overline { a d } \\) and \\( \overline { e h } \\). complete the statements. the length of \\( \overline { a d } \\) is units. the length of \\( \overline { e h } \\) is units. the sides have.

Explanation:

Step1: Calculate the length of \( \overline{AD} \)

Count the number of units between points \( A \) and \( D \). \( A \) and \( D \) are 3 units apart vertically. So, the length of \( \overline{AD} \) is 3 units.

Step2: Calculate the length of \( \overline{EH} \)

Since translation is a rigid transformation (it preserves lengths), and \( \overline{EH} \) corresponds to \( \overline{AD} \) (because \( EFGH \) is the translated image of \( ABCD \)). The length of \( \overline{EH} \) is also 3 units.

Step3: Compare the lengths of \( \overline{AD} \) and \( \overline{EH} \)

Since \( |\overline{AD}| = 3 \) and \( |\overline{EH}| = 3 \), the sides have the same length.

Answer:

The length of \( \overline{AD} \) is 3 units. The length of \( \overline{EH} \) is 3 units. The sides have the same length.