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 coordinates of \(K\)

The coordinates of \(K\) are \((-1,-9)\). Using the reflection rule \((x,y)\to(x, - y)\), for \(K(-1,-9)\), we have \(x=-1\) and \(y = - 9\). Then \(y\) becomes \(9\), so \(K'(-1,9)\).

Step3: Find the coordinates of \(L\)

The coordinates of \(L\) are \((4,-9)\). Using the reflection rule \((x,y)\to(x, - y)\), for \(L(4,-9)\), we have \(x = 4\) and \(y=-9\). Then \(y\) becomes \(9\), so \(L'(4,9)\).

Step4: Find the coordinates of \(M\)

The coordinates of \(M\) are \((4,0)\). Using the reflection rule \((x,y)\to(x, - y)\), for \(M(4,0)\), we have \(x = 4\) and \(y = 0\). Then \(y\) becomes \(0\) (since \(-0=0\)), so \(M'(4,0)\).

Step5: Find the coordinates of \(N\)

The coordinates of \(N\) are \((-1,0)\). Using the reflection rule \((x,y)\to(x, - y)\), for \(N(-1,0)\), we have \(x=-1\) and \(y = 0\). Then \(y\) becomes \(0\) (since \(-0 = 0\)), so \(N'(-1,0)\).

Answer:

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