Question

graph the image of m(-1, -7) after a reflection over the line y = -x.

Explanation:

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

The rule for reflecting a point \( (x, y) \) over the line \( y=-x \) is to swap the \( x \)- and \( y \)-coordinates and then multiply both by \( -1 \). So the transformation is \( (x, y)\to(-y, -x) \).

Step2: Apply the rule to \( M(-1, -7) \)

For the point \( M(-1, -7) \), let \( x = -1 \) and \( y = -7 \). Using the rule \( (x, y)\to(-y, -x) \), we substitute \( x \) and \( y \):
\( -y=-(-7) = 7 \) and \( -x=-(-1)=1 \). So the image of \( M(-1, -7) \) after reflection over \( y = -x \) is \( (7, 1) \).

Answer:

The image of \( M(-1, -7) \) after reflection over \( y=-x \) is the point \( (7, 1) \). To graph it, locate the point with \( x = 7 \) and \( y = 1 \) on the coordinate plane.