Question

the point (-4,1) is rotated 180 degrees counterclockwise using center (0,0). what are the coordinates of the image? select the correct answer below. a (-1,-4) b (-1,4) c (4,1) d (4,-1)

Explanation:

Step1: Recall rotation rule

When a point $(x,y)$ is rotated 180 degrees counter - clockwise about the origin $(0,0)$, the new coordinates $(x',y')$ are given by $(x',y')=(-x,-y)$.

Step2: Apply the rule

For the point $(-4,1)$, where $x = - 4$ and $y = 1$, we have $x'=-(-4)=4$ and $y'=-1$.

Answer:

D. $(4,-1)$