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

The point is (0, k). For reflection across x - axis, the rule is (x,y)→(x, - y). So (0,k)→(0, - k).

Step2: Analyze y - axis reflection

The rule for reflection across y - axis is (x,y)→( - x,y). For the point (0,k), - 0 = 0, so (0,k)→(0,k).

Step3: Consider y = x reflection

The rule for reflection across y = x is (x,y)→(y,x). So (0,k)→(k,0).

Step4: Analyze y = - x reflection

The rule for reflection across y=-x is (x,y)→( - y, - x). So (0,k)→( - k,0).

Answer:

a reflection of the point across the y - axis