90 DEGREE COUNTERCLOCKWISE ROTATION RULE

About the topic "90 degree counterclockwise rotation rule"

"90 degree counterclockwise rotation rule" is the stuff required to change each vertex of the given figure in order to rotate it 90 degree counter clockwise. 

Rule

When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x,y) to (-y,x) and graph the rotated figure.  

90 degree counterclockwise rotation rule - Practice problems 

To have better understanding on "90 degree counterclockwise rotation rule", let us look at some practice problems. 

Problem 1 : 

Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. If this triangle is rotated 90° counterclockwise, find the vertices of the rotated figure and graph.

Solution : 

Step 1 :

Here triangle is rotated 90° counterclockwise. 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)

F ( -4 , -2 ) ------------ F' ( 2 , -4 )

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

H ( -3 , 1 ) ------------ H' ( -1 , -3 )

Step 4 :

Vertices of the rotated figure are        

                       F' (2, -4) , G' (2, -2) and H' (-1, -3)  

GRAPH

Let us look at the next problem on "90 degree counterclockwise rotation rule"

Problem 2 : 

Let A (-4, 3), B (-4, 1), C (-3, 0), D (0, 2) and E (-3,4) be the vertices of a closed figure.If this figure is rotated 90° counterclockwise, find the vertices of the rotated figure and graph.

Solution : 

Step 1 :

Here the figure is rotated 90° counterclockwise. 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 ( -4 , 3 ) ------------ A' ( -3 , -4 )

B ( -4 , 1 ) ------------ B' ( -1 , -4 )

C ( -3 , 0 ) ------------ C' ( 0 , -3 )

D ( 0 , 2 ) ------------ D' ( -2 , 0 )

E ( -3 , 4 ) ------------ E' ( -4 , -3 )

Step 4 :

Vertices of the rotated figure are        

A' (-3, -4) , B' (-1, -4), C' (0, -3), D' (-2, 0) and E' (-4, -3)  

GRAPH

Let us look at the next problem on "90 degree counterclockwise rotation rule"

Problem 3 : 

Let D (-1, 2), E (-5, -1) and F (1, -1) be the vertices of a triangle.If the triangle is rotated 90° counterclockwise, find the vertices of the rotated figure and graph.

Solution : 

Step 1 :

Here the figure is rotated 90° counterclockwise. 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)

D ( -1 , 2 ) ------------ D' ( -2 , -1 )

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

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

Step 4 :

Vertices of the rotated figure are        

D' (-2, -1) , E' (1, -5) and F' (1, 1)  

GRAPH

Let us look at the next problem on "90 degree counterclockwise rotation rule"

Problem 4 : 

Let A (-5, 3), B (-4, 1), C (-2, 1) D (-1, 3) and E (-3,  4) be the vertices of a closed figure.If this figure is rotated 90° counterclockwise, find the vertices of the rotated figure and graph.

Solution : 

Step 1 :

Here the figure is rotated 90° counterclockwise. 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 ( -5 , 3 ) ------------ A' ( -3 , -5 )

B ( -4 , 1 ) ------------ B' ( -1 , -4 )

C ( -2 , 1 ) ------------ C' ( -1 , -2 )

D ( -1 , 3 ) ------------ D' ( -3 , -1 )

E ( -3 , 4 ) ------------ E' ( -4 , -3 )

Step 4 :

Vertices of the rotated figure are        

    A' (-3, -5) , B' (-1, -4), C' (-1, -2), D' (-3, -1) and E' (-4, -3)  

GRAPH

Let us look at the next problem on "90 degree counterclockwise rotation rule"

Problem 5 : 

Let R (-2, 4), S (-4, 4), T (-5, 3) U (-4, 2) and V (-2, 2) be the vertices of a closed figure.If this figure is rotated 90° counterclockwise, find the vertices of the rotated figure and graph.

Solution : 

Step 1 :

Here the figure is rotated 90° counterclockwise. 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 ( -2 , 4 ) ------------ R' ( -4 , -2 )

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

T ( -5 , 3 ) ------------ T' ( -3 , -5 )

U ( -4 , 2 ) ------------ U' ( -2 , -4 )

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

Step 4 :

Vertices of the rotated figure are        

R' (-4, -2) , S' (-4, -4), T' (-3, -5), U' (-2, -4) and E' (-2, -2)  

GRAPH

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