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 \((m,0)\), it becomes \((m,0)\) (since \(y = 0\)).
• Reflection across \(y -\)axis: \((x,y)\to(-x,y)\). For \((m,0)\), it becomes \((-m,0)\).
• Reflection across \(y=x\): \((x,y)\to(y,x)\). For \((m,0)\), it becomes \((0,m)\).
• Reflection across \(y =-x\): \((x,y)\to(-y,-x)\). For \((m,0)\), substitute \(x = m\) and \(y = 0\) into \((-y,-x)\), we get \((0,-m)\).

Since the reflection of the point \((m,0)\) across the line \(y=-x\) gives the point \((0,-m)\), the correct answer is the reflection across the line \(y =-x\).

Answer:

D. a reflection of the point across the line \(y = -x\)