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: Test point $(-4,-4)$

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

Step3: Test point $(-4,0)$

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

Step4: Test point $(0, - 4)$

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

Step5: Test point $(4,-4)$

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

Answer:

$(4,-4)$