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

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Howdo you rotate a figure 180 levels in anticlockwise or clockwise direction ~ above agraph?

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

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

1. Find the co-ordinates that the points derived on rotating the point out given listed below through 180° around 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 aboutthe origin, the brand-new position the the above points is.

(i) The brand-new position that the point A (3, 5) will be A" (-3, -5)

(ii) The brand-new position that the suggest B (-2, 7) will be B" (2, -7)

(iii) The new position the the allude C (-5, -8) will certainly be C" (5,8)

(iv) The new position the the point D (9, -4) will certainly be D" (-9,4)

2. Plot the pointM (-1, 4) on the graph paper and revolve it v 180° in the anticlockwisedirection about the origin O. Find the brand-new position the M.

Solution:


*

When rotated through 180° in the anticlockwise directionabout the origin O, then M (-1, 4) → M"" (1, -4).

3. draw a linesegment authorized the point P (-3, 1) and Q (2, 3) on the graph paper and rotateit v 180° around the beginning in anticlockwise direction.

Solution:


*

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

Now rotate PQ with 180° around 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 brand-new position of heat segment PQ is P"Q".

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

Solution:


*

On plot the points M (-2, 3) and also N (1, 4) top top the graphpaper to get the line segment MN.

Now, rotating MN v 180° about the origin O inanticlockwise direction, the brand-new position of clues 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. attract atriangle PQR by involvement the points ns (1, 4), Q (3, 1), R (2, -1) top top the graphpaper. Now rotate the triangle formed around the origin through 180° inclockwise direction.

Solution:


*

We acquire triangle PQR by plotting the suggest P (1, 4), Q (3,1), R (2, -1) top top the graph document when rotated with 180° around the origin. Thenew place of the suggest is:

P (1, 4) → P" (-1, -4)

Q (3, 1) → Q" (-3, -1)

R (2, -1) → R" (-2, 1)

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

Related concepts

● currently of Symmetry

● allude Symmetry

● Rotational the contrary

● stimulate of Rotational Symmetry

● species of symmetry

● Reflection

● enjoy of a allude in x-axis

● reflection of a point in y-axis

● have fun of a allude in origin

● Rotation

● 90 level Clockwise Rotation

● 90 level Anticlockwise Rotation

7th Grade mathematics Problems8th Grade math PracticeFrom 180 degree Rotation to house PAGE


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