The point ( -4,1 ) is rotated 180 degrees counterclockwise using center ( -3,0 ) what are the coordinates of the image

Answer 1

First, translate (-3, 0) to the origin: (-3, 0) → (-3+3, 0) = (0,0)

Translate (-4,1) in the same manner: (-4,1) → (-4+3, 1) = (-1,1)

Rotate (-1,0) counterclockwise 180° about the origin: (-1, 1) → (1,-1) [(x,y)→(-x,-y)]

Translate (1,-1) by "undoing" the original translation: (1,-1) → (1-3,-1) = (-2,-1)