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

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

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

Answer

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

Answer:

$(4,-4)$