Question

graph the image of m(-7, -9) 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 \( x \)- and \( y \)-coordinates and then multiply both by \( -1 \). So the transformation is \( (x, y) \to (-y, -x) \).

Step2: Apply the rule to \( M(-7, -9) \)

For the point \( M(-7, -9) \), let \( x = -7 \) and \( y = -9 \). Using the rule \( (x, y) \to (-y, -x) \), we substitute \( x \) and \( y \):
\( -y=-(-9) = 9 \) and \( -x=-(-7)=7 \). So the image of \( M(-7, -9) \) after reflection over \( y = -x \) is \( (9, 7) \).

Answer:

The image of \( M(-7, -9) \) after reflection over \( y = -x \) is the point \( (9, 7) \). To graph it, locate the point with \( x \)-coordinate 9 and \( y \)-coordinate 7 on the coordinate plane.