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

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.

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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