# What set of reflections would carry hexagon ABCDEF onto itself? Hexagon ABCDEF on the coordinate plane with point

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## Question:

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

When a point is reflected, it must be reflected across a line. The reflection of ABCDEF that carries it onto itself is:

D. y=x, x-axis, y=x, y-axis

Of the given options, (D) is correct.

The proof is as follows:

Using coordinate point A.

We have:

The first reflection in (D) is

This means that:

So, we have:

The next is across the x-axis.

The rule of this reflection is:

The next is

This means that:

The last is across the y-axis.

The rule of this reflection is:

Compare the end point to point A;

We can see that both points are the same i.e. (0,1)

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Hence, the set of reflections would carry hexagon ABCDEF onto itself is (d)