Question

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

Explanation:

Step1: Recall the rule for reflection over \(y = -x\)

The rule for reflecting a point \((x,y)\) over the line \(y=-x\) is \((x,y)\to(-y, -x)\). Let the pre - image of \(F\) be \((x,y)\) and the image be \((x',y')\). We know that \(x'=-y\) and \(y'=-x\).

Step2: Determine the coordinates of the image \(F\)

From the graph (assuming standard coordinate grid reading), the coordinates of the image \(F\) (after reflection) is \((2,-4)\). So \(x' = 2\) and \(y'=-4\).

Step3: Use the reflection formula to find the pre - image

Since \(x'=-y\) and \(y'=-x\), substituting \(x' = 2\) and \(y'=-4\) into the formulas:
If \(x'=-y\), then \(2=-y\Rightarrow y=-2\).
If \(y'=-x\), then \(-4=-x\Rightarrow x = 4\).

Answer:

\((4,2)\)