Question

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

Explanation:

Step1: Recall reflection rules

• Reflection across the \(x -\)axis: \((x,y)\to(x, - y)\). For the point \((0,k)\), it becomes \((0,-k)\).
• Reflection across the \(y -\)axis: \((x,y)\to(-x,y)\). For the point \((0,k)\), since \(x = 0\), \(-x=0\), and the point remains \((0,k)\).
• Reflection across the line \(y = x\): \((x,y)\to(y,x)\). For the point \((0,k)\), it becomes \((k,0)\).
• Reflection across the line \(y=-x\): \((x,y)\to(-y,-x)\). For the point \((0,k)\), it becomes \((-k,0)\).

Answer:

A reflection of the point across the \(y -\)axis.