Learn around the rules for 180 level rotation inanticlockwise or clockwise direction about the origin.

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Howdo you revolve a number 180 levels in anticlockwise or clockwise direction top top agraph?

Rotation that a point through 180°, about the origin when apoint M (h, k) is rotated about the beginning O v 180° in anticlockwise orclockwise direction, that takes the new position M" (-h, -k).

Worked-out examples on 180 level rotation about the origin:

1. Find the co-ordinates the the points acquired on rotating the point out 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 with 180° anticlockwise or clockwise aboutthe origin, the new position the the over points is.

(i) The new position the the suggest 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 brand-new position of the point D (9, -4) will certainly be D" (-9,4)

2. Plot the pointM (-1, 4) ~ above the graph document and revolve it v 180° in the anticlockwisedirection about the beginning O. Uncover the brand-new position of M.

Solution:


*

When rotated v 180° in the anticlockwise directionabout the beginning O, climate M (-1, 4) → M"" (1, -4).

3. attract a linesegment involvement the suggest P (-3, 1) and also Q (2, 3) top top the graph paper and rotateit through 180° about the beginning in anticlockwise direction.

Solution:


*

On plotting the points ns (-3, 1) and Q (2, 3) on the graph file to acquire the heat segment PQ.

Now turn PQ with 180° about the origin O in anticlockwise direction, the brand-new position of clues P and also Q is:

P (-3, 1) → P" (3, -1)

Q (2, 3) → Q" (-2, -3)

Thus, the new position of heat segment PQ is P"Q".

4. draw a linesegment MN authorized the suggest M (-2, 3) and also N (1, 4) on the graph paper. Rotateit v 180° in anticlockwise direction.

Solution:


*

On plotting the point out M (-2, 3) and also N (1, 4) ~ above the graphpaper to get the heat segment MN.

Now, rotating MN v 180° around the origin O inanticlockwise direction, the brand-new position of point out M and also N is:

M (-2, 3) → M" (2, -3)

N (1, 4) → N" (-1, -4)

Thus, the brand-new position of line segment MN is M"N".

5. draw atriangle PQR by joining the points ns (1, 4), Q (3, 1), R (2, -1) on the graphpaper. Now rotate the triangle formed around the origin through 180° inclockwise direction.

Solution:


*

We get triangle PQR by plotting the allude P (1, 4), Q (3,1), R (2, -1) ~ above the graph record when rotated with 180° around the origin. Thenew position of the suggest is:

P (1, 4) → P" (-1, -4)

Q (3, 1) → Q" (-3, -1)

R (2, -1) → R" (-2, 1)

Thus, the brand-new position the ∆PQR is ∆P’Q’R’.

Related principles

● lines of Symmetry

● allude Symmetry

● Rotational the opposite

● bespeak of Rotational Symmetry

● species of the contrary

● Reflection

● reflection of a suggest in x-axis

● enjoy of a allude in y-axis

● reflection of a suggest in beginning

● Rotation

● 90 degree Clockwise Rotation

● 90 degree Anticlockwise Rotation

7th Grade mathematics Problems8th Grade mathematics PracticeFrom 180 degree Rotation to residence PAGE


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