What is the result of reflecting a point through the origin?

What is the result of reflecting a point through the origin?

• A. (x,y) = (-x,y)
• B. (x,y) = (x,-y)
• C. (x,y) = (-x,-y)
• D. (x,y) = (y,x)

Answer: (C)

Reflecting a point through the origin involves moving it to a position that is directly opposite in relation to the origin on a coordinate plane. For any point represented by the coordinates (x, y), reflecting through the origin changes the signs of both coordinates. This means that the new coordinates will be (-x, -y). When the point (x, y) is reflected, it moves to the area of the plane that is both horizontally and vertically opposite to its original location. For example, if the original point is in the first quadrant, the reflected point will lie in the third quadrant. Therefore, the correct transformation for reflecting a point (x, y) through the origin is represented by the coordinates (-x, -y).

Reflecting a point through the origin involves moving it to a position that is directly opposite in relation to the origin on a coordinate plane. For any point represented by the coordinates (x, y), reflecting through the origin changes the signs of both coordinates.

This means that the new coordinates will be (-x, -y). When the point (x, y) is reflected, it moves to the area of the plane that is both horizontally and vertically opposite to its original location. For example, if the original point is in the first quadrant, the reflected point will lie in the third quadrant.

Therefore, the correct transformation for reflecting a point (x, y) through the origin is represented by the coordinates (-x, -y).