1. Marginnote 3 5 90 Degree Elbow
2. Marginnote 3 Windows
3. Marginnote 3 Review

Rule :

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

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Let us look at some examples to understand how 90 degree clockwise rotation can be done on a figure.

Example 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)

Example 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)

Example 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)

Marginnote 3 5 90 Degree Elbow

Example 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)

Example 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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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.

Example 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)

Example 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, 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)

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)

Example 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, 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)

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)

Example 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, 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)

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)

Example 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, 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)

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 :

Marginnote 3 Windows

Vertices of the rotated figure are

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

Apart from the stuff given above, if you need any other stuff, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

HCF and LCM word problems

Word problems on simple equations

Word problems on linear equations

Trigonometry word problems

Word problems on mixed fractrions

OTHER TOPICS

Ratio and proportion shortcuts

Marginnote 3 Review

Converting repeating decimals in to fractions

SBI!