# 90 DEGREE CLOCKWISE ROTATION ABOUT THE ORIGIN

The rule given below can be used to do a rotation of 90 degree about the origin. 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.

## 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) 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) 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) 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) 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), F'(3, 3)  Apart from the stuff given above, if you need any other stuff, please use our google custom search here.

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