Question

directions answer the question below to check your understanding and move forward in the over which line is the reflection happening? preimage image a(1,1) a(1, - 1) b(4,1) b(4, - 1) c(4,5) c(4, - 5) select the correct answer over the line y = 0 over the line y = x over the line x = 0 over the line y = -x

Explanation:

Step1: Analyze coordinate - change rule

When a point $(x,y)$ is reflected over the line $y = 0$ (the $x$ - axis), the transformation rule is $(x,y)\to(x, - y)$.
For point $A(1,1)$ which becomes $A'(1, - 1)$, $x$ - coordinate remains the same and $y$ - coordinate changes sign.
For point $B(4,1)$ which becomes $B'(4, - 1)$, $x$ - coordinate remains the same and $y$ - coordinate changes sign.
For point $C(4,5)$ which becomes $C'(4, - 5)$, $x$ - coordinate remains the same and $y$ - coordinate changes sign.

Step2: Check other reflection rules

• Reflection over $y=x$ has the rule $(x,y)\to(y,x)$.
• Reflection over $x = 0$ (the $y$ - axis) has the rule $(x,y)\to(-x,y)$.
• Reflection over $y=-x$ has the rule $(x,y)\to(-y,-x)$. These rules do not match the given pre - image and image points.

Answer:

Over the line $y = 0$