Question

Given that line segments are taken to line segments of the same length during rigid transformations, which transformation maps the line segment AB onto itself?

A) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → x-axis reflection
B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection
C) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
D) rotation counterclockwise of 180° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection

Answer 1

B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection

Rotate the line counterclockwise 90 degrees so that it's now facing top left and bottom right and the slope is negative going down. Now reflect it to the left over the y-axis which is the straight up vertical line. Then, reflect it back to the right and rotate it 270 degrees putting it back at the beginning so now it equals 360 degrees which is a full circle.

Answer 2

Correct Answer is C

Explanation:

rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection

Rotation counterclockwise of 90° (x, y) → (−y, x )

A(1, −2) → (2, 1)

B(4, 3) → (−3, 4)

x-axis Reflection (x, y) → (x, −y)

A(2, 1) → (2, −1)

B(−3, 4) → (−3, −4)

Rotation counterclockwise of 270° (x, y) → (y, −x )

A(2, −1) → (−1, −2)

B(−3, −4) → (−4, 3)

y-axis Reflection (x, y) → (−x, y)

A(−1, −2) → (1, −2)

B(−4, 3) → (4, 3)