180 Degree Rotation About The Origin - Onlinemath4all

180 DEGREE ROTATION ABOUT THE ORIGIN

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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.

Before Rotation (x, y)

After Rotation (-x, -y)

Video Lesson

Example 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)

Example 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 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)

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)

Example 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 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)

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)

Example 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 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)

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)

Example 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 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)

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)

You might like these

90-Degree Clockwise Rotation

90-Degree Counterclockwise Rotation

180-Degree Rotation about the Origin

270-Degree Clockwise Rotation

270-Degree Counterclockwise Rotation

Algebraic Representations of Rotation

Rotation Transformation

Rotation Transformation Matrix

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