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:

So, we have:

The next is

This means that:

So, we have:

The last is across the y-axis.

The rule of this reflection is:

So, we have:

Compare the end point to point A;

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

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

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