Which of the following is the rule for rotating the point with coordinates (x, y), 180° counterclockwise about the origin?
a. (x, y) → (y, x)
b. (x, y) → (y,-x)
c. (x, y) → (-y,-x)
d. (x, y) → (-x,-y)

  D.  (x, y) → (-x, -y)

Step-by-step explanation:

A. (x,y) → (y,x) . . . . reflects across the line y=x

B. (x,y) → (y,-x) . . . . rotates 90° CCW

C. (x,y) → (-y,-x) . . . . reflects across the line y=-x

D. (x,y) → (-x,-y) . . . . rotates 180° about the origin

The correct option is D.

Step-by-step explanation:

If a point rotating 180° counterclockwise about the origin, then the sign of each coordinate is changed.

Consider the coordinates of a point are (x,y).

If a (x,y) rotating 180° counterclockwise about the origin, then the rule of rotation is defined as

In which (x,y) is the coordinate pair of preimage and (-x,-y) is the coordinate pair of image.

Therefore the correct option is D.

If a point reflects across the line y=x , then

If a point rotated 90° clockwise, then

If a point reflects across the line y=-x, then

or

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step-by-step explanation: