Question

Given that a point, Z', is obtained after a 180° rotation, and its coordinates are Z'(3, 7), what were the coordinates of the pre-image point?

Answer 1

The pre-image point of Z'(3, 7) after a 180° rotation is Z(-3, -7), found by reversing the coordinates to their negatives.

Step-by-step explanation:

The student is asking about the coordinates of the original point before it was rotated 180° to become the point Z'(3, 7). In a 180° rotation around the origin, the coordinates of a point (x, y) become (-x, -y), because the rotation formula is:

• x' = -x
• y' = -y

Given the new coordinates Z'(3, 7), we can reverse the transformation:

• x = -3
• y = -7

Therefore, the coordinates of the pre-image point were Z(-3, -7).