Question

write the coordinates of the vertices after a reflection over the x - axis.

Explanation:

Step1: Recall the reflection rule

When reflecting a point \((x,y)\) over the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).

Step2: Find the original coordinates

From the graph, the original coordinates are \(B(-1,1)\), \(C(4,1)\), \(D(-6,-7)\).

Step3: Apply the reflection rule

For point \(B(-1,1)\):
Using the rule \((x,y)\to(x, - y)\), we get \(B'(-1,-1)\).
For point \(C(4,1)\):
Using the rule \((x,y)\to(x, - y)\), we get \(C'(4,-1)\).
For point \(D(-6,-7)\):
Using the rule \((x,y)\to(x, - y)\), we get \(D'(-6,7)\).

Answer:

\(B'(-1,-1)\), \(C'(4,-1)\), \(D'(-6,7)\)