Question

when g (3, -5) is reflected in the line y = x, the image is located at g ( select , select ).

Explanation:

Step1: Recall reflection over \( y = x \)

The rule for reflecting a point \((x, y)\) over the line \( y = x \) is to swap the \( x \)-coordinate and the \( y \)-coordinate. So, the image of \((x, y)\) is \((y, x)\).

Step2: Apply the rule to \( G(3, -5) \)

For the point \( G(3, -5) \), we swap the \( x \)-coordinate (which is 3) and the \( y \)-coordinate (which is -5). So the image \( G' \) will have coordinates \((-5, 3)\).

Answer:

The \( x \)-coordinate of \( G' \) is \(-5\) and the \( y \)-coordinate is \( 3 \), so \( G'(-5, 3) \).