What set of reflections would carry hexagon abcdef onto itself?

Asked by wiki @ 27/10/2020 in Mathematics viewed by 404 People

What set of reflections would carry hexagon ABCDEF onto itself? Hexagon ABCDEF on the coordinate plane with point
A at 0, 1,
point B at negative 1, 0,
point C at negative 2, 1,
point D at negative 2, 3,
point E at negative 1, 4,
and point F at 0, 3.
A. x-axis, y=x, x-axis, y=x
B. y-axis, x-axis, y-axis
C. x-axis, y-axis, y-axis
D. y=x, x-axis, y=x, y-axis

Answered by wiki @ 27/10/2020

You need an even number of reflections to get the original figure, leaving only A and D as potentially viable choices.

The reflection across the x-axis makes the tranformation (x, y) ⇒ (x, -y).
The reflection across the line y=x makse the transformation (x, y) ⇒ (y, x).
The two pairs of transformations of A give
(x, y) ⇒ (x, -y) ⇒ (-y, x) ⇒ (-y, -x) ⇒ (-x, -y) . . . . . not the original

The reflection across the y-axis makes the transformation (x, y) ⇒ (-x, y).
The two pairs of transformations of D give
(x, y) ⇒ (y, x) ⇒ (y, -x) ⇒ (-x, y) ⇒ (x, y) . . . . . . the original point

Selection D is appropriate.

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Asked by maham237 @ 13/01/2021 in Biology viewed by 328 persons

What set of reflections would carry hexagon abcdef onto itself?

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