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

• Reflection across x - axis: $(x,y)\to(x, - y)$. For point $(0,k)$, it becomes $(0, - k)$.

Step2: Reflection across y - axis

• Reflection across y - axis: $(x,y)\to(-x,y)$. For point $(0,k)$, $-0 = 0$, so it remains $(0,k)$.

Step3: Reflection across $y = x$

• Reflection across $y = x$: $(x,y)\to(y,x)$. For point $(0,k)$, it becomes $(k,0)$.

Step4: Reflection across $y=-x$

• Reflection across $y = - x$: $(x,y)\to(-y,-x)$. For point $(0,k)$, it becomes $(-k,0)$.

Answer:

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