90 DEGREE CLOCKWISE ROTATION ABOUT THE ORIGIN

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)

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