What set of reflections would carry hexagon abcdef onto itself? 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

The rule of reflection over x-axis ⇒⇒⇒ (x,y)→(x,-y)
The rule of reflection over y-axis ⇒⇒⇒ (x,y)→(-x,y)
The rule of reflection over y = x   ⇒⇒⇒ (x,y)→(y,x)

let the coordinate of any point of the hexagon is (m,n)

The correct sequence will make the same coordinates

which mean start with (m,n) and the finish is also (m,n)



Check option a- x-axis, y=x, x-axis, y=x
(m,n) → (m,-n) → (-n,m) → (-n,-m) → (-m,-n)  
Wrong set of reflections

Check option b- y-axis, x-axis, y-axis
(m,n) → (-m,n) → (-m,-n) → (m,-n)
Wrong set of reflections

Check option c- x-axis, y-axis, y-axis
(m,n) → (m,-n) → (-m,-n) → (m,-n)

Wrong set of reflections

Check option d- y=x, x-axis, y=x, y-axis
(m,n) → (n,m) → (n,-m) → (-m,n) → (m,n)
The correct set of reflections

So, the correct option is ⇒⇒ d- y=x, x-axis, y=x, y-axis