If the given figure is rotated 180° around the origin, what are the new coordinates of point Z?

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’.