Question

answer
a reflection over the y - axis
a reflection over the x - axis
a reflection over the line y = - 2
a reflection over the line y = -x + 1

Explanation:

Step1: Recall reflection rules

Reflection over y - axis changes sign of x - coordinate ($(x,y)\to(-x,y)$). Reflection over x - axis changes sign of y - coordinate ($(x,y)\to(x, - y)$). Reflection over horizontal line $y = k$ uses formula $(x,y)\to(x,2k - y)$. Reflection over line $y=-x + b$ uses transformation formulas based on perpendicular distance and mid - point properties.

Step2: Analyze each option visually

For reflection over y - axis, points on the figure would move to the opposite side of y - axis. For reflection over x - axis, points would move below or above x - axis. For reflection over $y=-2$, we use $(x,y)\to(x,-4 - y)$. For reflection over $y=-x + 1$, we use more complex transformation rules. Without seeing the original and transformed figure, we can analyze the general nature of these reflections. If the figure is symmetric about a horizontal line close to $y=-2$, a reflection over $y =-2$ is a likely candidate.

Answer:

a reflection over the line $y=-2$