Question

given abcd and aefg, describe a composition of rigid motions that maps abcd to aefg. choose the correct answer below. a. a reflection across the x - axis maps abcd to aefg. b. a 180° rotation about point a maps abcd to aefg. c. a translation that maps point b to point e maps abcd to aefg. d. a 90° counterclockwise rotation about point a maps abcd to aefg.

Explanation:

Step1: Analyze reflection across x - axis

A reflection across the x - axis changes the sign of the y - coordinates of all points. Looking at the figure, ABCD and AEFG do not have this relationship.

Step2: Analyze 180 - degree rotation about a point

A 180 - degree rotation about a point changes the orientation of the figure in a specific way. Here, the transformation from ABCD to AEFG is not a 180 - degree rotation about point A.

Step3: Analyze translation

A translation moves the figure without rotation or reflection. The transformation from ABCD to AEFG is not a simple translation.

Step4: Analyze 90 - degree counter - clockwise rotation

A 90 - degree counter - clockwise rotation about point A will map ABCD to AEFG. When we rotate a point (x,y) 90 - degree counter - clockwise about the origin (in this case, point A), the new coordinates (x',y') are given by (-y + a,x + b) where (a,b) are the coordinates of the center of rotation (point A). In the context of the figure, this rotation maps the vertices of ABCD to the vertices of AEFG.

Answer:

A. A 90° counterclockwise rotation about point A maps ABCD to AEFG.