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: Test each point

For point $(-4,-4)$:
If $x=-4$ and $y = - 4$, then $(-y,-x)=-(-4),-(-4)=(4,4)
eq(-4,-4)$.
For point $(-4,0)$:
If $x=-4$ and $y = 0$, then $(-y,-x)=(0,4)
eq(-4,0)$.
For point $(0,-4)$:
If $x = 0$ and $y=-4$, then $(-y,-x)=(4,0)
eq(0,-4)$.
For point $(4,-4)$:
If $x = 4$ and $y=-4$, then $(-y,-x)=-(-4),-4=(4,-4)$.

Answer:

$(4,-4)$