# WORKSHEET ON 90 DEGREE ANTICLOCKWISE ROTATION

## About the topic "Worksheet on 90 degree anticlockwise rotation"

"Worksheet on 90 degree anticlockwise rotation" is much useful to the students who would like to practice problems on "90 degree clockwise rotation"

## 90 degree counterclockwise rotation - 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.

## Worksheet on 90 degree anticlockwise rotation - Problems

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.

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.

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.

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.

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.

Here they are.

## Step by step solution

Let us look at step by step solution for  the problems given on "Worksheet on 90 degree anticlockwise rotation"

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 "Worksheet on 90 degree anticlockwise rotation"

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 "Worksheet on 90 degree anticlockwise rotation"

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 "Worksheet on 90 degree anticlockwise rotation"

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 "Worksheet on 90 degree anticlockwise rotation"

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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