Question

1. the quadrilateral math was rotated 90 degrees counterclockwise followed by a translation to produce the quadrilateral math. click in the table below to show which side lengths are equal to the lengths of the given line segments. | | a | b | c | d | |---|---|---|---|---| | line segment ma | | | ☑ | | | line segment at | | | | ☑ |

Explanation:

Step1: Recall Transformation Properties

Rotations and translations are rigid transformations. Rigid transformations preserve side lengths (and angle measures). So, corresponding sides of the original quadrilateral (MATH) and the transformed quadrilateral (M'A'T'H') are equal. Also, the red quadrilateral (with sides a, b, c, d) is the image of MATH after rotation and translation, so its sides correspond to MATH's sides.

Step2: Analyze Line Segment MA

MA is a side of MATH. After rigid transformations, its length should equal the length of the corresponding side in the red quadrilateral. From the table, for MA, the checked box is for c, meaning c corresponds to MA (since rigid transformations preserve length).

Step3: Analyze Line Segment AT

AT is a side of MATH. The checked box for AT is for d, so d corresponds to AT (again, due to rigid transformations preserving side lengths).

Answer:

For line segment MA, the equal side length is c (since rigid transformations preserve length, MA corresponds to c). For line segment AT, the equal side length is d (same reason, AT corresponds to d). So the table entries show MA = c and AT = d, which is correct because rotations and translations (rigid transformations) preserve side lengths.