Final answer:
An angle measuring 78° in a coordinate plane retains its measure when reflected across the line y = x, translated horizontally or vertically, or reflected across the y-axis. Translations and rotations do not change angle measurements.
Step-by-step explanation:
The angle of 78° on a coordinate plane has certain properties when subjected to various transformations. Let's examine each statement and determine which ones are correct:
- A. If it is reflected across the line y = x, it will still measure 78°.
- B. If it is translated 22 units down, it will no longer measure 78°.
- C. If it is rotated 180° about the origin, it will no longer measure 78°.
- D. If it is reflected across the y-axis, it will no longer measure 78°.
- E. If it is translated 26 units to the left, it will still measure 78°.
- F. If it is rotated 90° about the origin, it will still measure 78°.
Correct statements regarding the angle are:
- Statement A is true because reflection across the line y = x does not change the measure of angles.
- Statement E is true because translation, either horizontally or vertically, does not affect the magnitude of angles.
- Statement D is true because reflection across the y-axis will result in an angle that retains its original measure but is oriented differently (it will be a congruent angle).
Statements B, C, and F are incorrect. Translations do not affect angle measures, thus statement B is incorrect. Rotation by 180° or any other angle will not alter the measure of an angle, thus statement C is incorrect. Similarly, rotation by 90° also does not change the measure of an angle, making statement F incorrect.