Question

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

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

Answer:

$(4, - 4)$