Question

which point would map onto itself after a reflection across the line y = -x? (-4, -4) (-4, 0) (0, -4) (4, -4)

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ across the line $y = -x$ is $(x,y)\to(-y,-x)$.

Step2: Check each option

For point $(-4,-4)$: applying the rule $(-4,-4)\to -(-4),-(-4)=(4,4)
eq(-4,-4)$.
For point $(-4,0)$: applying the rule $(-4,0)\to(0,4)
eq(-4,0)$.
For point $(0, - 4)$: applying the rule $(0,-4)\to(4,0)
eq(0,-4)$.
For point $(4,-4)$: applying the rule $(4,-4)\to -(-4),-4=(4,-4)$.

Answer:

$(4,-4)$