Question

what is the pre - image of vertex ( a ) if the image shown on the graph was created by a reflection across the ( y ) - axis?
( (-8,-6) )
( (-6,8) )
( (8,6) )
( (6,-8) )

Explanation:

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

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

Step2: Determine the coordinates of \(A'\)

From the graph, the coordinates of \(A'\) are \((6,8)\).

Step3: Apply the reflection rule to find the pre - image

Let the pre - image of \(A'\) be \((x,y)\). Using the rule \((x,y)\to(-x,y)\) for reflection across the \(y\) - axis. If \(-x = 6\) and \(y = 8\), then \(x=-6\) and \(y = 8\).

Answer:

\((-6,8)\) (the second option)