Question

which of the following reflective symmetries apply to the nonagon?
symmetry
applies to the figure?
reflective symmetry over the line ( y = -x )
reflection symmetry over the line ( y = -\frac{2}{3}x )

Explanation:

Step1: Understand reflective symmetry

Reflective symmetry means that when a figure is reflected over a line, the reflected image coincides with the original figure.

Step2: Check symmetry over \(y = -x\)

For a non - regular nonagon (9 - sided polygon), if we consider the line \(y=-x\). A non - regular nonagon may or may not have this symmetry. But in the given graph, when we consider the reflection over \(y =-x\), the two halves of the nonagon (divided by the line \(y=-x\)) do not match exactly.

Step3: Check symmetry over \(y=-\frac{2}{3}x\)

When we consider the reflection over the line \(y =-\frac{2}{3}x\), the two halves of the nonagon (divided by the line \(y =-\frac{2}{3}x\)) do not match exactly.

Answer:

Reflective symmetry over the line \(y=-x\): No
Reflective symmetry over the line \(y =-\frac{2}{3}x\): No