Question

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

Explanation:

Step1: Identify coordinates of \( A' \)

From the graph, vertex \( A' \) has coordinates \( (6, 8) \) (assuming the grid and position, as the y - axis value is 8 and x - axis is 6).

Step2: Apply reflection over y - axis rule

The rule for reflection over the y - axis is \( (x,y)\to(-x,y) \). For the point \( A'(6, 8) \), applying the rule: \( x = 6\) becomes \( - 6\), and \( y = 8\) remains \( 8 \). So the pre - image (the point before reflection) of \( A' \) after reflection over y - axis is \( (-6,8) \).

Answer:

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