Mathematics
Find the co-ordinates of the points obtained on rotating the following points through 180° about the origin :
(i) (3, 4)
(ii) (3, -4)
(iii) (-3, 4)
(iv) (-3, -4)
(v) (0, 4)
Symmetry
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Answer
(i) When a point P(x, y) is rotated through 180°, about the origin O, we get the point P' = (-x, -y).
For the point (3, 4), after the rotation, the new coordinates become (-3, -4).
(ii) When a point P(x, y) is rotated through 180°, about the origin O, we get the point P' = (-x, -y).
For the point (3, -4), after the rotation, the new coordinates become (-3, 4).
(iii) When a point P(x, y) is rotated through 180°, about the origin O, we get the point P' = (-x, -y).
For the point (-3, 4), after the rotation, the new coordinates become (3, -4).
(iv) When a point P(x, y) is rotated through 180°, about the origin O, we get the point P' = (-x, -y).
For the point (-3, -4), after the rotation, the new coordinates become (3, 4).
(v) When a point P(x, y) is rotated through 180°, about the origin O, we get the point P' = (-x, -y).
For the point (0, 4), after the rotation, the new coordinates become (0, -4).
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