Question

the figure that results from a transformation is called the image. figure abcd is translated to get its image, figure efgh. look at ad and eh. complete the statements. the length of ad is 4 units. the length of eh is 4 units. the sides have the same length.

Explanation:

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

On the coordinate - grid, for \( \overline{AD} \), since it is a vertical side. If we assume the coordinates of \( A\) and \( D\) (using the grid, if we consider the distance between two points on a vertical line \( (x_1,y_1)\) and \( (x_1,y_2)\) is \( |y_2 - y_1|\)). Counting the number of units from \( A\) to \( D\) vertically, we get \( 4\) units.

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

Since translation is a rigid transformation. A rigid transformation (translation in this case) preserves the shape and size of the figure. That is, if figure \( ABCD\) is translated to get figure \( EFGH\), then corresponding sides are congruent. \( \overline{AD}\) and \( \overline{EH}\) are corresponding sides. So, the length of \( \overline{EH}\) is equal to the length of \( \overline{AD}\).

Answer:

The length of \( \overline{AD}\) is \( 4\) units. The length of \( \overline{EH}\) is \( 4\) units. The sides have the same length.