180 Degree Rotation

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:

180 Degree Rotation

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:

180 Degree Rotation about the Origin

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:

Rotate a Figure 180 Degrees

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:

Rotated through 180° about the Origin

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

Lines of Symmetry

Point Symmetry

Rotational Symmetry

Order of Rotational Symmetry

Types of Symmetry

Reflection

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







7th Grade Math Problems

8th Grade Math Practice

From 180 Degree Rotation to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Successor and Predecessor | Successor of a Whole Number | Predecessor

    Jul 29, 25 12:59 AM

    Successor and Predecessor
    The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number…

    Read More

  2. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 28, 25 01:52 PM

    Volume of a Cuboids
    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  3. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  4. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  5. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More