Questions: 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

Solution Steps

We need to determine which reflection of the point \((0, k)\) will produce an image at the same coordinates, \((0, k)\).

1. Reflection across the \(x\)-axis:

   • The reflection of a point \((x, y)\) across the \(x\)-axis is \((x, -y)\).
   • For the point \((0, k)\), the reflection would be \((0, -k)\).

2. Reflection across the \(y\)-axis:

   • The reflection of a point \((x, y)\) across the \(y\)-axis is \((-x, y)\).
   • For the point \((0, k)\), the reflection would be \((0, k)\).

3. Reflection across the line \(y = x\):

   • The reflection of a point \((x, y)\) across the line \(y = x\) is \((y, x)\).
   • For the point \((0, k)\), the reflection would be \((k, 0)\).

4. Reflection across the line \(y = -x\):

   • The reflection of a point \((x, y)\) across the line \(y = -x\) is \((-y, -x)\).
   • For the point \((0, k)\), the reflection would be \((-k, 0)\).

From the analysis, the only reflection that results in the point \((0, k)\) remaining at \((0, k)\) is the reflection across the \(y\)-axis.

Final Answer