the point z(4,-2) is rotated 180 about the origin. what is the image of z?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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).