Question

a point has the coordinates (m, 0) and m ≠ 0. which reflection of the point will produce an image located at (0, -m)? 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 $(m,0)$, it becomes $(m,0)$ (since $y = 0$).
• Reflection across $y - axis$: $(x,y)\to(-x,y)$. For point $(m,0)$, it becomes $(-m,0)$.
• Reflection across $y=x$: $(x,y)\to(y,x)$. For point $(m,0)$, it becomes $(0,m)$.
• Reflection across $y=-x$: $(x,y)\to(-y,-x)$. For point $(m,0)$, substitute $x = m$ and $y = 0$ into the rule. We get $(-0,-m)=(0,-m)$.

Answer:

D. a reflection of the point across the line $y=-x$