Question

interactive practice: work with sequences of transformations and congruence
perform a sequence of transformations on figure efgh.
efgh ≅ efgh
which single transformation shows that the figures are congruent?
a rotation 180° around the origin
a reflection across the x - axis
a rotation 90° counterclockwise around the origin
a translation 5 units to the right

Explanation:

1. Recall the properties of congruent - figure transformations:

• A rotation of 180° around the origin changes the sign of both the x - and y - coordinates of each point.
• A reflection across the x - axis changes the sign of the y - coordinate of each point.
• A rotation of 90° counter - clockwise around the origin swaps the x and y coordinates and changes the sign of one of them.
• A translation moves the figure without changing its orientation or shape.

1. Analyze the given figures:

• For a reflection across the x - axis, the y - values of the points of figure EFGH would change sign. But the orientation of the figure in the x - direction would not match the orientation of E''F''G''H''.
• For a 90° counter - clockwise rotation around the origin, the orientation of the figure would be different from E''F''G''H''.
• For a translation 5 units to the right, the figure would just move horizontally and not change its orientation in the way E''F''G''H'' is oriented.
• A 180° rotation around the origin changes the orientation of the figure in a way that matches the orientation of E''F''G''H''.

Answer:

A. A rotation 180° around the origin