In this blog we are going to tell you about What Set Of Reflections Would Carry Hexagon ABCDEF Onto Itself, so read this blog carefully to get the complete information.

Hexagon ABCDEF on the coordinate plane with a 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

Answer: (D.) y=x, x-axis, y=x, y-axis

Answer Explanation:

When a point is reflected, it must be reflected across a line so the reflection of ABCDEF that carries it onto itself is- y=x, x-axis, y=x, y-axis. We can prove this by using coordinate point A.

We have, A = (0,1)

The first reflection in (D) is given by, y=x

It implies that (x,y) → (y,x)

So we will get, (0,1) → (1,0)

The next is across the x-axis and by the rule of this reflection we will get,

(x,y) → (x,-y)

This implies that (1,0) → (1,0)

The next is, y = x

which means, (x,y) → (y,x)

 and we will get, (1,0) → (0,1)

The last reflection is across the y-axis so by the rule of reflection we will get,

(x,y) → (-x,y)

By which we have, y = x

So on comparing the end of point A we can observe that both the points are the same which is (0,1). Therefore the set of reflections that will carry the hexagon ABCDEF onto itself is y=x, x-axis, y=x, and y-axis.

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Conclusion

We hope you got your answer and understood why this set of reflections will carry hexagon ABCDEF onto itself as explained above.

We Hope this blog is sufficient enough to provide the information What Set Of Reflections Would Carry Hexagon ABCDEF Onto Itself. Thanks for reading this blog.