A 180^(∘) rotation counterclockwise about the origin will change the coordinates of the points such that r_((180^(∘),O))(x,y)=(- x, - y).
(4,-1)
Practice makes perfect
Let's start by graphing the given coordinates so that we can see the point.
When a point is rotated 180^(∘) counterclockwise about the origin, the coordinates of the image point will change in the following way.
r_((180^(∘),O))(x,y)=(- x, - y)
Using this rule and the coordinates of the given point, we can find the x- and y-coordinates of the image point.
r_((180^(∘),O))(-4,1)=(4, - 1)
Knowing the coordinates of the image point, we can draw the given point and its rotation.
