Question

figure abcdef was reflected across the line y = -x to create figure abcdef. what are the coordinates of the pre - image of f? (-2,4) (4,2) (2,-4) (-4,-2)

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: Identify coordinates of $F'$

From the graph, the coordinates of $F'$ are $(2, - 4)$.

Step3: Apply inverse - reflection rule

Let the coordinates of $F$ be $(x,y)$. Using the reflection rule $(x,y)\to(-y,-x)$ in reverse. If $-y = 2$ and $-x=-4$, then $y=-2$ and $x = 4$.

Answer:

$(4,2)$