Question

A point has the coordinates (m, 0) and m ≠ 0.

Which reflection of the point will produce an image located at (0, –m)?

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

Answer 1

its d

Explanation:

Answer 2

The correct answer is:

A reflection across the line y = -x.

Explanation:

When a point is reflected across the x-axis, it negates the y-coordinate, but they stay in the same position. This is not the case in this ordered pair.

When a point is reflected across the y-axis, it negates the x-coordinate, but they stay in the same position. This is not the case in this ordered pair.

When a point is reflected across the line y=x, it switches the x- and y-coordinates, but neither is negated. This is not the case in this ordered pair.

When a point is reflected across the line y = -x, it negates both coordinates and switches them. Algebraically, this is represented by (x, y)→(-y, -x). Our point (m, 0) becomes (0, -m); the first thing we see is that the coordinates are switched. Additionally, m is negated. While 0 is not negated, this is because there is no negative 0. This is the correct answer.