Question

Which of these statements are correct about an angle measuring 78° in a coordinate plane? Select three that apply.

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, will still measure 78°.
F) If it is rotated 90° about the origin, will still measure 78°.

Answer 1

The correct answer is option A,C and E. The correct statements about an angle measuring 78° in a coordinate plane are A) it will still measure 78° if reflected across the line y = x, E) it will still measure 78° if translated 26 units to the left, and C) it will still measure 78° if rotated 180° about the origin.

Step-by-step explanation:

The correct statements about an angle measuring 78° in a coordinate plane are:

• If it is reflected across the line y = x, it will still measure 78°. Reflection across the line y = x swaps the x and y coordinates of points forming the angle but does not change the measure of the angle itself.
• If it is translated 26 units to the left, it will still measure 78°. A translation involves moving every point of a figure the same distance in a specified direction, which does not alter the angle measure.
• If it is rotated 180° about the origin, it will still measure 78°. A rotation of 180° about the origin will result in the angle pointing in the opposite direction, but the measure of the angle remains unchanged at 78°.

It is important to note that while the orientation or position of an angle can change due to transformations such as reflection, translation, or rotation, the measure of the angle itself is preserved. Thus, the correct options are A, E, and C.