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

Correct choice is C

Explanation:

Points A and B have coordinates (1,-2) and (4,3), respectively.

1. Rotation counterclockwise of 90° about the origin has a rule:

(x,y)→(-y,x).

Then the image of point A is point A'(2,1) and the image of point B is point B'(-3,4).

2. Refection about the x-axis has a rule:

(x,y)→(x,-y).

Then the image of point A' is point A''(2,-1) and the image of point B' is point B''(-3,-4).

3. Rotation counterclockwise of 270° about the origin has a rule:

(x,y)→(y,-x).

Then the image of point A'' is point A'''(-1,-2) and the image of point B'' is point B'''(-4,3).

4. Refection about the y-axis has a rule:

(x,y)→(-x,y).

Then the image of point A''' is point A(1,-2) and the image of point B''' is point B(4,3).