Question

a point has the coordinates (0, k), where k ≠ 0. which reflection of the point will produce an image at the same coordinates, (0, k)? a reflection of the point across the x - axis a reflection of the point across the line y = x a reflection of the point across the line y = -x a reflection of the point across the y - axis

Explanation:

Step1: Recall reflection rules

The rule for reflecting a point $(x,y)$ across the $x -$axis is $(x,-y)$. For a point $(0,k)$ reflected across the $x -$axis, the image is $(0, - k)$. The rule for reflecting a point $(x,y)$ across the $y -$axis is $(-x,y)$. For a point $(0,k)$ reflected across the $y -$axis, the image is $(0,k)$. The rule for reflecting a point $(x,y)$ across the line $y = x$ is $(y,x)$. For a point $(0,k)$ reflected across the line $y=x$, the image is $(k,0)$. The rule for reflecting a point $(x,y)$ across the line $y=-x$ is $(-y,-x)$. For a point $(0,k)$ reflected across the line $y =-x$, the image is $(-k,0)$.

Answer:

A reflection of the point across the $y$-axis