Question

what line of reflection will give an image with point e at (4,1)? y=x x=0 y=-x y=1

Explanation:

Step1: Recall reflection rules

Reflection over $y = x$ swaps the $x$ and $y$ - coordinates of a point. Reflection over $x = 0$ (the $y$ - axis) changes the sign of the $x$ - coordinate. Reflection over $y=-x$ negates both coordinates and swaps them. Reflection over $y = 1$ changes the $y$ - coordinate based on its distance from $y = 1$.

Step2: Analyze point E

Assume point E has coordinates $(1,4)$ (since reflection over $y = x$ swaps coordinates). If E has coordinates $(1,4)$, reflecting it over the line $y = x$ will give $E'$ with coordinates $(4,1)$.

Answer:

A. $y=x$