Question

graph the image of g(-5, 4) after a reflection over the y-axis.

Explanation:

Step1: Recall reflection over y - axis rule

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

Step2: Apply the rule to point \(G(-5,4)\)

For the point \(G(-5,4)\), using the reflection rule over the \(y\) - axis, we substitute \(x = - 5\) into \(-x\). So, \(-x=-(-5) = 5\) and \(y\) remains \(4\). So the image of \(G(-5,4)\) after reflection over the \(y\) - axis is \((5,4)\).

Step3: Graph the point

To graph the point \((5,4)\), we move 5 units to the right along the \(x\) - axis (since \(x = 5\)) and 4 units up along the \(y\) - axis (since \(y = 4\)) and mark the point.

Answer:

The image of \(G(-5,4)\) after reflection over the \(y\) - axis is the point \((5,4)\), and it is graphed at the coordinates \((5,4)\) on the given coordinate plane.