Question

solve the problems.
1 the gray figure has been transformed in different ways.
tell whether each statement is true or false.
a. figure a is a reflection of the gray figure. □ true □ false
b. figure b is a rotation of the gray figure. □ true □ false
c. figure c is a translation of the gray figure. □ true □ false
d. figure d is a reflection of the gray figure. □ true □ false
e. figure e is a rotation of the gray figure. □ true □ false

Explanation:

Part a

To determine if Figure A is a reflection of the gray figure, we check the mirror - image property. A reflection flips the figure over a line. By comparing the shape and orientation of Figure A with the gray figure, we can see that Figure A is a reflection (horizontal or vertical flip that matches the gray figure's shape when flipped). So the statement is True.

For a rotation, the figure is turned around a point. By analyzing the shape and orientation of Figure B relative to the gray figure, we find that Figure B can be obtained by rotating the gray figure (e.g., 90 - degree rotation or other angle that preserves the shape and changes the orientation appropriately). So the statement is True.

A translation moves the figure without changing its shape, size, or orientation. Figure C has a different orientation compared to the gray figure, so it is not a translation. The statement is False.

Answer:

a. $\square$True $\square$False (with the True box checked)

Part b