# 180 DEGREE ROTATION ABOUT THE ORIGIN

"180 degree rotation about the origin" is the stuff about rotating a figure 180 degrees either in the clockwise or counter-clockwise direction.

## 180 degree rotation about the origin - Rule When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x,y) to (-x,-y) and graph the rotated figure.

## 180 degree rotation about the origin - Practice problems

To have better understanding on "180 degree rotation about the origin", let us look at some practice problems.

Problem 1 :

Let P (-2, -2), Q (1, -2) R (2, -4) and S (-3, -4) be the vertices of a four sided closed figure. If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the given is rotated 180° about the origin. So the rule that we have to apply here is (x , y) -------> (-x , -y)

Step 2 :

Based on the rule given in step 1, we have to find the vertices of the rotated figure

Step 3 :

(x , y) ----------> (-x , -y)

P ( -2 , -2 ) ------------ P' ( 2 , 2 )

Q ( 1 , -2 ) ------------ Q' ( -1 , 2 )

R ( 2, -4 ) ------------ R' ( -2, 4 )

S ( -3 , -4 ) ------------ S' ( 3 , 4 )

Step 4 :

Vertices of the rotated figure are

P' (2, 2) , Q' (-1, 2), R' (-2, 4) and S' (3, 4)

GRAPH Let us look at the next problem on "180 degree rotation about the origin"

Problem 2 :

Let K (1, 4), L (-1, 2), M (1, -2) and N (3, 2) be the vertices of a four sided closed figure.If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 180° about the origin. So the rule that we have to apply here is (x , y) -------> (-x , -y)

Step 2 :

Based on the rule given in step 1, we have to find the vertices of the rotated figure

Step 3 :

(x , y) ----------> (-x , -y)

K ( 1 , 4  ) ------------ K' ( -1 , -4 )

L ( -1 , 2 ) ------------ L' ( 1 , -2 )

M ( 1 , -2 ) ------------ M' ( -1 , 2 )

N ( 3 , 2 ) ------------ N' ( -3 , -2 )

Step 4 :

Vertices of the rotated figure are

K' (-1, -4) , L' (1, -2), M' (-1, 2) and N' (-3, -2)

GRAPH Let us look at the next problem on "180 degree rotation about the origin"

Problem 3 :

Let E (1, 5), F (1, 1), G (5, 1) and H (5, 5) be the vertices of a four sided closed figure.If the figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 180° about the origin. So the rule that we have to apply here is (x , y) -------> (-x , -y)

Step 2 :

Based on the rule given in step 1, we have to find the vertices of the rotated figure

Step 3 :

(x , y) ----------> (-x , -y)

E ( 1 , 5 ) ------------ E' ( -1 , -5 )

F ( 1 , 1 ) ------------ F' ( -1 , -1 )

G ( 5 , 1 ) ------------ G' ( -5 , -1 )

H ( 5 , 5 ) ------------ H' ( -5 , -5 )

Step 4 :

Vertices of the rotated figure are

E' (-1, -5) , F' (-1, -1), G' (-5, -1) and H' (-5, -5)

GRAPH Let us look at the next problem on "180 degree rotation about the origin"

Problem 4 :

Let E (5, 4), F (1, 4), G (0, 2) and H (4, 2) be the vertices of a four sided closed figure.If the figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 180° about the origin. So the rule that we have to apply here is (x , y) -------> (-x , -y)

Step 2 :

Based on the rule given in step 1, we have to find the vertices of the rotated figure

Step 3 :

(x , y) ----------> (-x , -y)

E ( 5 , 4 ) ------------ E' ( -5 , -4 )

F ( 1 , 4 ) ------------ F' ( -1 , -4 )

G ( 0 , 2 ) ------------ G' ( 0 , -2 )

H ( 4 , 2 ) ------------ H' ( -4 , -2 )

Step 4 :

Vertices of the rotated figure are

E' (-5, -4) , F' (-1, -4), G' (0, -2) and H' (-4, -2)

GRAPH Let us look at the next problem on "180 degree rotation about the origin"

Problem 5 :

Let K (0, -4), L (4, -4), M (4, -2) and N (1, -2) be the vertices of a four sided closed figure.If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 180° about the origin. So the rule that we have to apply here is (x , y) -------> (-x , -y)

Step 2 :

Based on the rule given in step 1, we have to find the vertices of the rotated figure

Step 3 :

(x , y) ----------> (-x , -y)

K ( 0 , -4  ) ------------ K' ( 0 , 4 )

L ( 4 , -4 ) ------------ L' ( -4 , 4 )

M ( 4 , -2 ) ------------ M' ( -4 , 2 )

N ( 1 , -2 ) ------------ N' ( -1 , 2 )

Step 4 :

Vertices of the rotated figure are

K' (0, 4) , L' (-4, 4), M' (-4, 2) and N' (-1, 2)

GRAPH We hope that the students would have understood the stuff given on "180 degree rotation about the origin"

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