Question

symmetry:
□x - axis
□y - axis
□origin
□none of these

Explanation:

Step1: Check x - axis symmetry

If a figure is symmetric about the x - axis, for every point \((x,y)\) on the figure, the point \((x, - y)\) is also on the figure. Looking at the diamond - shaped figure, if we take a point \((x,y)\) above the x - axis, its reflection \((x,-y)\) below the x - axis is also on the figure.

Step2: Check y - axis symmetry

If a figure is symmetric about the y - axis, for every point \((x,y)\) on the figure, the point \((-x,y)\) is also on the figure. For any point \((x,y)\) on the right - hand side of the y - axis, its reflection \((-x,y)\) on the left - hand side of the y - axis is on the figure.

Step3: Check origin symmetry

If a figure is symmetric about the origin, for every point \((x,y)\) on the figure, the point \((-x,-y)\) is also on the figure. If we take a point \((x,y)\) in the first quadrant, its reflection \((-x,-y)\) in the third quadrant is on the figure.

Answer:

x - axis, y - axis, origin