The coordinates of the image is (4,-1) that is option D) is correct.
According to the question we have been given that
the point to be rotated = (-4,1)
center = (-3,0)
Rotation = 180° counterclockwise.
Note that when the point is rotated 180° counterclockwise then the coordinate of the image point will be
(x , y ) = (-x , - y)
For the coordinates of the image first we translate the center to the origin that is
(-3,0) = (-3+3,0) = (0,0)
Now we will do same for the point that is,
(-4 , 1) = (-4+3 , 1) = (-1,1)
Now the points are (-1,1). Thus the image will be
(-1,1) = (-(-1), -1) = (1,-1)
Now undoing the original translation :
(1,-1) = (1+3,-1) = (4,-1)
Hence the coordinates of the image is (4,-1) that is option D) is correct.
Learn more about translation here : https://brainly.com/question/12861087
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