Question

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

Explanation:

Step1: Recall the reflection rule over the x - axis

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

Step2: Find the original coordinates

From the graph:

• For point \(K\), the original coordinates are \((-1,-9)\).
• For point \(L\), the original coordinates are \((4,-9)\).
• For point \(M\), the original coordinates are \((4,0)\).
• For point \(N\), the original coordinates are \((-1,0)\).

Step3: Apply the reflection rule

• For \(K(-1,-9)\), after reflection over the \(x\) - axis: \((-1,-(-9))=(-1,9)\).
• For \(L(4,-9)\), after reflection over the \(x\) - axis: \((4,-(-9))=(4,9)\).
• For \(M(4,0)\), after reflection over the \(x\) - axis: \((4,-0)=(4,0)\).
• For \(N(-1,0)\), after reflection over the \(x\) - axis: \((-1,-0)=(-1,0)\).

Answer:

\(K'(-1,9)\)
\(L'(4,9)\)
\(M'(4,0)\)
\(N'(-1,0)\)