ROTATION OF 90 DEGREES ABOUT THE ORIGIN

"Rotation of 90 degrees about the origin" is a counter-clockwise rotation of 90 degrees.

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

Rotation of 90 degrees about the origin - Practice problems

To have better understanding on "Rotation of 90 degrees about the origin", 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° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here triangle is rotated 90° about the origin. 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 "Rotation of 90 degrees about the origin"

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° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 90° about the origin. 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 "Rotation of 90 degrees about the origin"

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° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 90° about the origin. 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 "Rotation of 90 degrees about the origin"

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° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 90° about the origin. 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 "Rotation of 90 degrees about the origin"

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° about the origin, find the vertices of the rotated figure and graph.

Solution :

Step 1 :

Here the figure is rotated 90° about the origin. 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 We hope that the students would have understood the stuff given on "Rotation of 90 degrees about the origin"

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