Question

a point has the coordinates (0, k), where k ≠ 0. which reflection of the point will produce an image at the same coordinates, (0, k)? a reflection of the point across the line y = -x 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

Explanation:

Step1: Recall reflection rules

The point is on the y - axis with coordinates (0, k).

Step2: Analyze each reflection

• Reflection across \(y=-x\): The rule for reflecting a point \((x,y)\) across \(y =-x\) is \((x,y)\to(-y,-x)\). For \((0,k)\), it becomes \((-k,0)\).
• Reflection across \(x - axis\): The rule for reflecting a point \((x,y)\) across the \(x - axis\) is \((x,y)\to(x,-y)\). For \((0,k)\), it becomes \((0, - k)\).
• Reflection across \(y - axis\): The rule for reflecting a point \((x,y)\) across the \(y - axis\) is \((x,y)\to(-x,y)\). For the point \((0,k)\), \(-x = 0\) and \(y=k\), so the image is \((0,k)\).
• Reflection across \(y = x\): The rule for reflecting a point \((x,y)\) across \(y = x\) is \((x,y)\to(y,x)\). For \((0,k)\), it becomes \((k,0)\).

Answer:

a reflection of the point across the \(y\) - axis