The orientation of the image following a rotation of 180° clockwise or anticlockwise is the same
When PQ is rotated 180° around point R° and the resulting segment is the same as PQ, then; R could be located at the midpoint of PQ
The reason the location of R, given above is correct is presented as follows;
The coordinates of the image of a preimage point (x, y) following a 180° rotation about the origin, is the point (-x, -y)
Given that the resulting segment following reflection of PQ, which is P'Q' is the same as PQ, we have;
Let (x, y) represent the coordinate of point P, and let (-x, -y) represent the coordinate of the point Q, we have;
The coordinate of point P' = the coordinate of the point Q
The coordinate of point Q' = the coordinate of the point P
The slope of the line PQ = (y - (-y))/(x - (-x)) = y/x = (y - 0)/(x - 0)
Therefore, the line PQ passes through the origin and the distance of the from the origin to P is equal to the distance of the origin to Q, given that P is located at (x, y), and Q at (-x, -y), such that the origin O, is the midpoint of PQ
Which gives;
When PQ is rotated about a point, R, located at the midpoint of PQ, the resulting segment Q'P' has the same coordinates as the segment PQ
Therefore, R, could be located at the midpoint of PQ
Learn more about rotation transformation here:
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