# 90 DEGREE CLOCKWISE ROTATION ABOUT THE ORIGIN

## About the topic "90 degree clockwise rotation about the origin"

"90 degree clockwise rotation about the origin" is the stuff which is required to the students who study math in the grade level 6.

## 90 degree clockwise rotation about the origin - Rule When we rotate a figure of 90 degrees clockwise about the orign, each point of the given figure has to be changed from (x,y) to (y,-x) and graph the rotated figure.

## 90 degree clockwise rotation about the origin  - Practice problems

To have better understanding on "90 degree clockwise rotation about the origin", let us look at some practice problems.

Problem 1 :

Let K (-4, -4), L (0, -4), M (0, -2) and N(-4, -2) be the vertices of a rectangle. If this rectangle is rotated 90° clockwise, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here triangle is rotated 90° clockwise. So the rule that we have to apply here is (x , y) -------> (y , -x)

Step 2 :

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

Step 3 :

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

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

L ( 0 , -4 ) ------------ L' ( -4 , 0 )

M ( 0 , -2 ) ------------ M' ( -2 , 0 )

N ( -4 , -2 ) ------------ N' ( -2 , 4 )

Step 4 :

Vertices of the rotated figure are

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

GRAPH Let us look at the next problem on "90 degree clockwise rotation about the origin"

Problem 2 :

Let R (-3, 5), S (-3, 1), T (0, 1), U (0, 2), V (-2, 2) and W (-2, 5) be the vertices of a closed figure.If this figure is rotated 90° clockwise, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 90° clockwise. So the rule that we have to apply here is (x , y) -------> (y , -x)

Step 2 :

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

Step 3 :

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

R ( -3 , 5 ) ------------ R' ( 5 , 3 )

S ( -3 , 1 ) ------------ S' ( 1 , 3 )

T ( 0 , 1 ) ------------ T' ( 1 , 0 )

U ( 0 , 2 ) ------------ U' ( 2 , 0 )

V ( -2 , 2 ) ------------ V' ( 2 , 2 )

W ( -2 , 5 ) ------------ W' ( 5 , 2 )

Step 4 :

Vertices of the rotated figure are

R' (5, 3) , S' (1, 3), T' (1, 0), U' (2, 0), V' (2, 2) and W' (5, 2)

GRAPH Let us look at the next problem on "90 degree clockwise rotation about the origin"

Problem 3 :

Let P (-1, -3), Q (3, -4), R (4, 0) and S (0, -1) be the vertices of a closed figure. If the figure is rotated 90° clockwise, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 90° clockwise. So the rule that we have to apply here is (x , y) -------> (y , -x)

Step 2 :

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

Step 3 :

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

P ( -1 , -3 ) ------------ P' ( -3 , 1 )

Q ( 3 , -4 ) ------------ Q' ( -4 , -3 )

R ( 4 , 0 ) ------------ R' ( 0 , -4 )

S ( 0 , -1 ) ------------ S' ( -1 , 0 )

Step 4 :

Vertices of the rotated figure are

P' (-3, 1) , Q' (-4, -3), R ( 0, -4) and S' (-1, 0)

GRAPH Let us look at the next problem on "90 degree clockwise rotation about the origin"

Problem 4 :

Let T (1, -3), U (5, -5), V (3, -3) and W (5, -1) be the vertices of a closed figure.If this figure is rotated 90° clockwise, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 90° clockwise. So the rule that we have to apply here is (x , y) -------> (y , -x)

Step 2 :

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

Step 3 :

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

T ( 1 , -3 ) ------------ T' ( -3 , -1 )

U ( 5 , -5 ) ------------ U' ( -5 , -5 )

V ( 3 , -3 ) ------------ V' ( -3 , -3 )

W ( 5 , -1 ) ------------ W' ( -1 , -5 )

Step 4 :

Vertices of the rotated figure are

T' (-3, -1) , U' (-5, -5), V' (-3, -3) and  W' (-1, -5)

GRAPH Let us look at the next problem on "90 degree clockwise rotation about the origin"

Problem 5 :

Let A (-2, 4), B (2, 4), C (1, 3) D (2, 2), E (-2, 2) and F (-3, 3)  be the vertices of a closed figure.If this figure is rotated 90° clockwise, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 90° clockwise. So the rule that we have to apply here is (x , y) -------> (-y , x)

Step 2 :

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

Step 3 :

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

A ( -2 , 4 ) ------------ A' ( 4 , 2 )

B ( 2 , 4 ) ------------ B' ( 4 , -2 )

C ( 1 , 3 ) ------------ C' ( 3 , -1 )

D ( 2 , 2 ) ------------ D' ( 2 , -2 )

E ( -2 , 2 ) ------------ E' ( 2 , 2 )

F ( -3 , 3 ) ------------ F' ( 3 , 3 )

Step 4 :

Vertices of the rotated figure are

A' (4, 2) , B' (4, -2), C' (3, -1), D' (2, -2), E' (2, 2) and F' (3, 3)

GRAPH We hope that the students would have understood the stuff given on "90 degree clockwise rotation about the origin"

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