Question

Which algebraic rule describes the 180° counter-clockwise rotation about the origin?

Answer 1

The algebraic rule describes the 180° counter-clockwise rotation about the origin =======> Answer: Rule for 180 degrees Counter-Clockwise Rotation =======> ( X , Y ) =========> ( - X, - Y ) ====> Make X + Y Signs Opposite.

Rotations Counter-Clockwise:

Rotation of 90 degrees ========> Switch X + Y, Make Y Opposite.

Rotation of 270 degrees ======> ( X, Y ) ===> ( Y, - X ) ==> Switch X + Y, Make X Opposite.

Hope that helps!!!! : )

Answer 2

`(x,y)\Rightarrow (-x,-y)`

Explanation:

We are asked to write the algebraic rule that describes the 180° counter-clockwise rotation about the origin.

When we rotate a point 180 degrees about origin the coordinates of point changes their sign.

The point
`(x,y)` after a rotation of 180 degrees about origin changes to
`(-x,-y)`.

The rule for this rotation is:
`(x,y)\Rightarrow (-x,-y)`

Therefore, our required expression would be
`(x,y)\Rightarrow (-x,-y)`.