Problem


When point $F($ is reflected in the line $y=-x$, the image is located at $F^{\prime}(-7,1)$.

Answer

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Answer

Final Answer: The original point $F$ before reflection was $\boxed{(1,7)}$.

Steps

Step 1 :When point $F$ is reflected in the line $y=-x$, the image is located at $F^{\prime}(-7,1)$.

Step 2 :The reflection of a point across the line $y=-x$ results in a new point where the x and y coordinates are swapped and their signs are reversed.

Step 3 :So, if the reflected point $F'$ is $(-7,1)$, then the original point $F$ should be $(1,7)$.

Step 4 :Therefore, the original point $F$ before reflection was indeed $(1,7)$.

Step 5 :Final Answer: The original point $F$ before reflection was $\boxed{(1,7)}$.

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