Question

what are the coordinates of the image of vertex p after a reflection across the line y = -x? (-1, -3) (3, -1) (1, 3) (-3, 1)

Explanation:

Step1: Find the coordinates of vertex \( F \)

From the graph, the coordinates of vertex \( F \) are \((-3, -1)\).

Step2: Apply the rule for reflection across the line \( y=-x \)

The rule for reflection across the line \( y =-x \) is \((x,y)\to(-y,-x)\).
For the point \((-3,-1)\), substitute \( x=-3 \) and \( y =-1 \) into the rule:
\( x'=-y=-(-1) = 1\) and \( y'=-x=-(-3)=3\).

Answer:

\((1,3)\) (the third option)