Learn about the rules for 180 degree rotation in anticlockwise or clockwise direction about the origin.
How do you rotate a figure 180 degrees in anticlockwise or clockwise direction on a graph?
Rotation of a point through 180°, about the origin when a point M (h, k) is rotated about the origin O through 180° in anticlockwise or clockwise direction, it takes the new position M' (-h, -k).
Worked-out examples on 180 degree rotation about the origin:
1. Find the co-ordinates of the points obtained on rotating the points given below through 180° about the origin. i) A (3, 5)
(ii) B (-2, 7)
(iii) C (-5, -8)
(iv) D (9, -4)
Solution:
When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is.
(i) The new position of the point A (3, 5) will be A' (-3, -5)
(ii) The new position of the point B (-2, 7) will be B' (2, -7)
(iii) The new position of the point C (-5, -8) will be C' (5, 8)
(iv) The new position of the point D (9, -4) will be D' (-9, 4)
2. Plot the point M (-1, 4) on the graph paper and rotate it through 180° in the anticlockwise direction about the origin O. Find the new position of M.
Solution: When rotated through 180° in the anticlockwise direction about the origin O, then M (-1, 4) → M'' (1, -4).
3. Draw a line segment joining the point P (-3, 1) and Q (2, 3) on the graph paper and rotate it through 180° about the origin in anticlockwise direction.
Solution: On plotting the points P (-3, 1) and Q (2, 3) on the graph paper to get the line segment PQ.
Now rotate PQ through 180° about the origin O in anticlockwise direction, the new position of points P and Q is:
P (-3, 1) → P' (3, -1)
Q (2, 3) → Q' (-2, -3)
Thus, the new position of line segment PQ is P'Q'.
4. Draw a line segment MN joining the point M (-2, 3) and N (1, 4) on the graph paper. Rotate it through 180° in anticlockwise direction.
Solution: plotting the points M (-2, 3) and N (1, 4) on the graph paper to get the line segment MN.
Now, rotating MN through 180° about the origin O in anticlockwise direction, the new position of points M and N is:
M (-2, 3) → M' (2, -3)
N (1, 4) → N' (-1, -4)
Thus, the new position of line segment MN is M'N'. 5. Draw a triangle PQR by joining the points P (1, 4), Q (3, 1), R (2, -1) on the graph paper. Now rotate the triangle formed about the origin through 180° in clockwise direction.
Solution: We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is:
P (1, 4) → P' (-1, -4)
Q (3, 1) → Q' (-3, -1)
R (2, -1) → R' (-2, 1)
Thus, the new position of ∆PQR is ∆P’Q’R’.
