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

The rule for reflecting a point \((x,y)\) across the \(y\)-axis is \((x,y)\to(-x,y)\).

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

From the graph, assume the coordinates of \(A'\) (after reflection) is \((6,8)\) (by observing the position on the grid).

Step3: Apply the inverse of the reflection rule

If \((x',y')=(6,8)\) is the image after \(y\)-axis reflection, then using the inverse of \((x,y)\to(-x,y)\) (i.e., to find the pre - image \((x,y)\) from the image \((x',y')\) we use \(x=-x'\), \(y = y'\)).
Substituting \(x' = 6\) and \(y'=8\), we get \(x=-6\) and \(y = 8\). So the pre - image is \((-6,8)\).

Answer:

B. \((-6,8)\)