Question

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

Explanation:

Step1: Recall the reflection rule

When reflecting a point \((x,y)\) across the line \(y = -x\), the transformation rule is \((x,y)\to(-y,-x)\).

Step2: Apply the rule to point \(F(1,-3)\)

For point \(F\) with \(x = 1\) and \(y=-3\), substitute into the rule:
\(-y=-(-3) = 3\) and \(-x=-1\).
So the image of \(F(1,-3)\) after reflection across \(y=-x\) is \((3,-1)\).

Answer:

(3, -1)