Students who feel difficult to solve the rotation problems can refer to this page and learn the techniques so easily. Rotation in Maths is turning an object in a circular motion on any origin or axis. Any object can be rotated in both directions ie., Clockwise and Anticlockwise directions. Generally, there are three rotation angles around the origin, 90 degrees, 180 degrees, and 270 degrees. One of the rotation angles ie., 270° rotates occasionally around the axis. Both 90° and 180° are the common rotation angles. Check out this article and completely gain knowledge about ** 180-degree rotation about the origin **with solved examples.

## 180 Degree Rotation Around the Origin

When the point **M (h, k)** is rotating through 180°, about the origin in a Counterclockwise or clockwise direction, then it takes the new position of the point** M’ (-h, -k)**. So, the 180-degree rotation about the origin in both directions is the same and we make both h and k negative.

Before Rotation |
After Rotation |

(h, k) | (-h,-k) |

### Rule of 180° Rotation

- If the point (x,y) is rotating about the origin in 180-degrees clockwise direction, then the new position of the point becomes (-x,-y).
- If the point (x,y) is rotating about the origin in 180-degrees counterclockwise direction, then the new position of the point becomes (-x,-y).

### Worked-Out Problems on 180-Degree Rotation About the Origin

**Example 1:**

Determine the vertices taken on rotating the points given below through 180° about the origin.

(i) P (6, 9)

(ii) Q (-5, 8)

(iii) R (-2, -6)

(iv) S (1, -3)

**Solution:**

The rule of 180-degree rotation is ‘when the point M (h, k) is rotating through 180°, about the origin in a Counterclockwise or clockwise direction, then it takes the new position of the point M’ (-h, -k)’. By applying this rule, here you get the new position of the above points:

(i) The new position of the point P (6, 9) will be P’ (-6, -9)

(ii) The new position of the point Q (-5, 8) will be Q’ (5, -8)

(iii) The new position of the point R (-2, -6) will be R’ (2, 6)

(iv) The new position of the point S (1, -3) will be S’ (-1, 3)

**Example 2:**

Put the point A (2, 3) on the graph paper and rotate it through 180° about the origin O. Calculate the new position of A’.

**Solution:**

Given coordinate is A = (2,3) after rotating the point towards 180 degrees about the origin then the new position of the point is **A’ = (-2, -3)** as shown in the above graph.

### FAQs on 180 Degree Clockwise & Anticlockwise Rotation

**1. What is the rule for 180° Rotation?**

The rule for a rotation by 180° about the origin is (x,y)→(−x,−y).

**2. Is turning 180 degrees clockwise different from turning 180 degrees counterclockwise?**

Yes, both are different but the formula or rule for 180-degree rotation about the origin in both directions clockwise and anticlockwise is the same.

**3. How the 180 degrees look like?**

The measure of 180 degrees in an angle is known as Straight angles. Then the 180 degrees look like a **Straight Line. **