Question

question 1-3
when point m is reflected over the line y = -x, the image is located at m(-6,2) what are the coordinates of pre - image m?
○ m(-2,2)
○ m(2,-6)
○ m(-2,6)
○ m(-6,6)

Explanation:

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

The rule for reflecting a point \((x, y)\) over the line \( y=-x \) is \((x, y)\to(-y, -x)\). So if the image is \( M'(-6, 2) \), let the pre - image \( M=(x, y) \). Then we have the equations \(-y=-6\) and \(-x = 2\).

Step2: Solve for \( x \) and \( y \)

From \(-y=-6\), multiply both sides by \(- 1\) to get \( y = 6\). From \(-x=2\), multiply both sides by \(-1\) to get \( x=-2\). So the coordinates of \( M \) are \((-2,6)\).

Answer:

\( M(-2, 6) \)