What set of reflections would carry hexagon ABCDEF onto itself?a. y=x, x-axis, y=x, y-axisb. x-axis, y=x, x-axis, y=xc. y-axis, x-axis, y-axisd. x-axis, y-axis, y-axis
Accepted Solution
A:
Answer: option a. y=x, x-axis, y=x, y-axis.
Explanation:
1) Take a general point with coordinates (a,b)
2) Reflecting it over the line y = x translates it to (b,a)
3) Reflecting (b,a) over the x-axis translates it to (b,-a)
4) Reflecting (b,-a) over y = x translates it to (-a,b)
5) Reflecting (-a,b) over the y-axis translates it to (a,b)
Therefore, that set of reflections have translated (a,b) to the same place (a,b), concluding that that set of reflections carries the hexagon ABCDEF onto itself.