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: \((x,y)\to(x, - y)\)
• Reflection across \(y -\)axis: \((x,y)\to(-x,y)\)
• Reflection across \(y = x\): \((x,y)\to(y,x)\)
• Reflection across \(y=-x\): \((x,y)\to(-y,-x)\)

Step2: Apply rules to \((m,0)\)

• For reflection across \(x -\)axis: \((m,0)\to(m,0)\)
• For reflection across \(y -\)axis: \((m,0)\to(-m,0)\)
• For reflection across \(y = x\): \((m,0)\to(0,m)\)
• For reflection across \(y=-x\): \((m,0)\to(0,-m)\)

Answer:

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