Question

graph the image of q(-1, 6) after a reflection over the line y = x.

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, if we have a point \( (a, b) \), its image after reflection over \( y = x \) is \( (b, a) \).

Step2: Apply the rule to \( Q(-1, 6) \)

For the point \( Q(-1, 6) \), we swap the \( x \)-coordinate (\( -1 \)) and the \( y \)-coordinate (\( 6 \)). So the image of \( Q \) after reflection over \( y = x \) is \( (6, -1) \).

To graph this, we locate the point \( (6, -1) \) on the coordinate plane: we move 6 units to the right along the \( x \)-axis and 1 unit down along the \( y \)-axis.

Answer:

The image of \( Q(-1, 6) \) after reflection over \( y = x \) is the point \( (6, -1) \).