180 Clockwise About The Origin

180 Degree Rotation

Learn most the rules for 180 caste rotation in anticlockwise or clockwise management almost the origin.

How do yous rotate a figure 180 degrees in anticlockwise or clockwise direction on a graph?

Rotation of a point through 180°, almost the origin when a point Grand (h, k) is rotated about the origin O through 180° in anticlockwise or clockwise direction, information technology takes the new position M' (-h, -k).

Worked-out examples on 180 degree rotation most the origin:

i. Observe 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, vii)

(three) 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 indicate A (iii, 5) volition exist A' (-3, -5)

(ii) The new position of the point B (-2, 7) will be B' (two, -7)

(three) The new position of the point C (-five, -8) will be C' (5, 8)

(iv) The new position of the point D (ix, -4) will be D' (-9, 4)

2. Plot the indicate Thou (-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, -four).

3. Describe a line segment joining the point P (-3, ane) and Q (2, 3) on the graph paper and rotate it through 180° about the origin in anticlockwise management.

Solution:

On plotting the points P (-3, 1) and Q (2, three) on the graph newspaper to get the line segment PQ.

At present rotate PQ through 180° about the origin O in anticlockwise direction, the new position of points P and Q is:

P (-3, one) → P' (3, -i)

Q (2, 3) → Q' (-2, -three)

Thus, the new position of line segment PQ is P'Q'.

iv. Draw a line segment MN joining the bespeak M (-2, 3) and Northward (1, 4) on the graph newspaper. Rotate it through 180° in anticlockwise management.

Solution:

On plotting the points Thou (-2, three) and North (ane, 4) on the graph newspaper to get the line segment MN.

Now, rotating MN through 180° almost the origin O in anticlockwise direction, the new position of points M and N is:

M (-2, 3) → One thousand' (2, -3)

Due north (one, four) → N' (-1, -4)

Thus, the new position of line segment MN is M'N'.

five. Depict a triangle PQR by joining the points P (1, 4), Q (3, 1), R (2, -1) on the graph paper. At present rotate the triangle formed about the origin through 180° in clockwise management.

Solution:

We go triangle PQR by plotting the point P (one, 4), Q (3, 1), R (2, -ane) on the graph newspaper when rotated through 180° about the origin. The new position of the signal is:

P (1, four) → P' (-1, -4)

Q (3, 1) → Q' (-3, -one)

R (2, -1) → R' (-2, one)

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 Signal in 10-axis

● Reflection of a Point in y-axis

● Reflection of a point in origin

● Rotation

● 90 Degree Clockwise Rotation

● 90 Caste Anticlockwise Rotation

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180 Clockwise About The Origin,

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