Question

a point has the coordinates (0, k). 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 y - axis a reflection of the point across the line y = x a reflection of the point across the line y = -x

Explanation:

Step1: Recall reflection rules

The point is $(0,k)$.

Step2: Analyze reflection across x - axis

For a point $(x,y)$ reflected across the $x$-axis, the new point is $(x, - y)$. For $(0,k)$ it becomes $(0,-k)$.

Step3: Analyze reflection across y - axis

For a point $(x,y)$ reflected across the $y$-axis, the new point is $(-x,y)$. For $(0,k)$, $- 0=0$, so the point remains $(0,k)$.

Step4: Analyze reflection across $y = x$

For a point $(x,y)$ reflected across the line $y = x$, the new point is $(y,x)$. For $(0,k)$ it becomes $(k,0)$.

Step5: Analyze reflection across $y=-x$

For a point $(x,y)$ reflected across the line $y=-x$, the new point is $(-y,-x)$. For $(0,k)$ it becomes $(-k,0)$.

Answer:

B. a reflection of the point across the y - axis