Question

what are the coordinates of the image of vertex g after a reflection across the line ( y = x )? ( (-4,-5) ) ( (4,5) ) ( (-5,4) ) ( (5,-4) )

Explanation:

Step1: Recall the rule for reflection across \(y = x\)

When a point \((a,b)\) is reflected across the line \(y=x\), the new coordinates are \((b,a)\).

Step2: Identify the coordinates of point \(G\)

From the graph, the coordinates of vertex \(G\) are \((4,-5)\).

Step3: Apply the reflection rule

Using the rule \((a,b)\to(b,a)\) with \(a = 4\) and \(b=-5\), we get \((-5,4)\).

Answer:

\((-5,4)\)