Question

What set of reflections would carry hexagon ABCDEF onto itself?

Hexagon ABCDEF on the coordinate plane with point A at 1, 0, point B at 0, 1, point C at 1, 2, point D at 3, 2, point E at 4, 1, and point F at 3, 0.

y=x, x-axis, y=x, y-axis
x-axis, y=x, x-axis, y=x
y-axis, x-axis, y-axis
x-axis, y-axis, y-axis

Answer 1

test one by one./

Answer 2

You pick A as sample, now, test the first option
\(R_{y=x}(A)=R_{y=x} (1,0) = (0,1) \)

Then, \(R_{x-axis} (0,1) = (0,-1)\)

Next, \(R_{y=x}(0,-1) = (-1,0)\)

Lastly, \(R_{y-axis}(-1,0) = (-(-1), 0) = (1,0)\)
Hence, the first option maps A (1,0) to itself (1,0)
you test one more point to see what if the first option apply on that point or not. (100 % yes) then first option is the answer