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You need to determine the coordinates of symmetric point to origin, hence, first you need to determine the quadrant the point z is in.
Since x coordinate is positive and y coordinate is negative, the point z is in quadrant 4, hence, the symmetric point is in quadrant 2.
Since the image of the point z is in quadrant 2, the x coordinate is negative and y coordinate is positive such that:
Notice that x and y coordinates of image point z'(-4,2) have opposite values to the coordinates of original point z(4,-2).
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