Question

answer
a reflection over the line $y=-x + 9$
a reflection over the line $x=-1$
a reflection over the x - axis
a reflection over the line $y=x + 4$

Explanation:

Step1: Recall reflection rules

For a point $(x,y)$ reflected over the line $x = a$, the new - point is $(2a - x,y)$. For a point $(x,y)$ reflected over the line $y=-x + b$, the new point is $(b - y,b - x)$. For a point $(x,y)$ reflected over the $x$ - axis, the new point is $(x,-y)$. For a point $(x,y)$ reflected over the line $y=x + c$, the new point is $(y - c,x + c)$.

Step2: Analyze the symmetry of the given figure

If we consider the line $x=-1$, we can observe that for each point on one side of the line $x = - 1$, there is a corresponding point on the other side of the line $x=-1$ at the same $y$ - value and at an equal distance from the line $x=-1$.
If we consider the line $y=-x + 9$, we can check some key - points of the figure. Let's take a general point $(x,y)$ on the figure and apply the transformation $(b - y,b - x)$ with $b = 9$. The figure does not match the result of this transformation.
For reflection over the $x$ - axis, the $y$ - coordinates of all points would change their signs. The figure does not show this transformation.
For reflection over the line $y=x + 4$, applying the transformation $(y - 4,x + 4)$ to points on the figure does not result in the given figure.

Answer:

a reflection over the line $x=-1$