Question

write the coordinates of the vertices after a reflection over the y - axis

Explanation:

Step1: Recall the rule for reflection over the y - axis

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

Step2: Find the coordinates of the original points

From the graph, \(K(-8, - 5)\), \(L(-8,5)\), \(M(-6,5)\), \(N(-6,-5)\).

Step3: Apply the reflection rule

For point \(K(-8,-5)\):
Using the rule \((x,y)\to(-x,y)\), when \(x = - 8\) and \(y=-5\), then \(K'=(8,-5)\).
For point \(L(-8,5)\):
Using the rule \((x,y)\to(-x,y)\), when \(x=-8\) and \(y = 5\), then \(L'=(8,5)\).
For point \(M(-6,5)\):
Using the rule \((x,y)\to(-x,y)\), when \(x=-6\) and \(y = 5\), then \(M'=(6,5)\).
For point \(N(-6,-5)\):
Using the rule \((x,y)\to(-x,y)\), when \(x=-6\) and \(y=-5\), then \(N'=(6,-5)\).

Answer:

\(K'(8,-5)\), \(L'(8,5)\), \(M'(6,5)\), \(N'(6,-5)\)