Final answer:
Translations and reflections do not affect angle measurements, nor do rotations around the origin. The correct statements about the angle measuring 78° undergoing these transformations are A, E, and F. These actions will not alter the angle's measurement to any value other than 78°.
Step-by-step explanation:
A 78° angle in a coordinate plane has some properties that remain unchanged under certain transformations. Specifically:
A. If a 78° angle is reflected across the line y = x, the angle measure will remain 78°. This reflection is like flipping the angle over the line y = x, but the size of the angle does not change.
B. If it is translated 22 units down, the 78° angle will still measure 78°. Translation is just sliding the figure up, down, left, or right, and does not affect angle measures.
C. If it is rotated 180° about the origin, the angle measure of 78° remains the same. Rotation about the origin also does not change the size of angles; it merely moves them within the plane.
D. If it is reflected across the y-axis, the angle measure of 78° remains the same. Reflections across an axis do not change the size of the angle but can flip its orientation.
E. If it is translated 26 units to the left, the angle measure of 78° remains the same. Like other translations, this shift moves the angle but does not change its size.
F. If it is rotated 90° about the origin, the angle measure of 78° does change its orientation, but the angle size remains 78°. Thus, the measurement of the angle is still preserved after rotation.
An angle measuring 78° in a coordinate plane will maintain its measurement after being reflected across the line y = x, translated 26 units to the left, or rotated 90° about the origin.