Do you think a sequence of translations across the x- or y-axis and/or reflections on a figure could result in the same image as

Question

7nadin3 [17]

3 years ago

6

Do you think a sequence of translations across the x- or y-axis and/or reflections on a figure could result in the same image as

a 90-degree clockwise rotation?

Mathematics

2 answers:

SVEN [57.7K] · Answer 1 · 2022-08-11T01:23:11+03:00

SVEN [57.7K]3 years ago

6 0

Answer:

The short answer is yes

Step-by-step explanation:

denis-greek [22] · Answer 2 · 2022-08-11T03:02:47+03:00

Answer: No, it is not possible.

If you reflect over the x axis first, then the y axis next, then you'll perform a 180 degree rotation. The same can be said if you do a y axis reflection first, then x axis reflection next.

In order to perform a 90 degree clockwise rotation, we would need to reflect over the line y = x and y = 0 in either order. The line y = 0 is the same as the x axis.

The line y = x splits the first quadrant into two equal pieces. The angle between y = x and y = 0 is 45 degrees which doubles to 90 degrees. So we can see the relationship between the angle of rotation and the angle between the lines of reflection.