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: **

On 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’.

● **Related Concepts **

**● Order of Rotational Symmetry**

**● Reflection of a Point in x-axis**

**● Reflection of a Point in y-axis **

**● Reflection of a point in origin **

**● Rotation**

**● 90 Degree Clockwise Rotation**

**● 90 Degree Anticlockwise Rotation**

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