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 \(F(1,-3)\)

Here \(x = 1\) and \(y=-3\). Substitute into the rule: \(-y=-(-3) = 3\) and \(-x=-1\).

Answer:

\((3, - 1)\) (the second option)