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 x - axis: For a point \((x,y)\), the image is \((x, -y)\).
• Reflection across y - axis: For a point \((x,y)\), the image is \((-x,y)\).
• Reflection across line \(y = x\): For a point \((x,y)\), the image is \((y,x)\).
• Reflection across line \(y=-x\): For a point \((x,y)\), the image is \((-y, -x)\).

Step2: Apply rules to point \((0,k)\)

• For reflection across x - axis: The point \((0,k)\) becomes \((0,-k)

eq(0,k)\) (unless \(k = 0\), but generally not the same).

• For reflection across y - axis: The point \((0,k)\) becomes \((- 0,k)=(0,k)\) (since \(-0 = 0\)).
• For reflection across line \(y = x\): The point \((0,k)\) becomes \((k,0)

eq(0,k)\) (unless \(k = 0\), but generally not the same).

• For reflection across line \(y=-x\): The point \((0,k)\) becomes \((-k,0)

eq(0,k)\) (unless \(k = 0\), but generally not the same).

Answer:

a reflection of the point across the y - axis