EXAMPLES OF ROTATION OF 2D SHAPES WHEN CENTER OF ROTATION IS GIVEN

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If we rotate the 2d shape about origin, we will follow the rules given below about the angle that we are rotating.

Step 1 :

If center of rotation is something else than origin, we have to draw the horizontal and vertical lines in order to consider we have origin at the specified point.

Step 2 :

From the center of rotation, we have to move horizontally and vertically to get each vertices of the 2d shape.

Step 3 :

Moving right, x-coordinate = positive

Moving left, x-coordinate = negative

Moving up, y-coordinate = positive

Moving down, y-coordinate = negative

Rotating the shape means moving them around a fixed point. There are two directions

i) Clockwise

ii) Counter clockwise (or) Anti clockwise

The shape itself stays exactly the same, but its position in the space will change.

90° clockwise

90° counter clockwise

180°

270° clockwise

270° counter clockwise

(x, y) ==> (y, -x)

(x, y) ==> (-y, x)

(x, y) ==> (-x, -y)

(x, y) ==> (-y, x)

(x, y) ==> (y, -x)

Rotate each of the shapes below as instructed, using the origin, (0, 0), as the centre of rotation.

Problem 1 :

Solution:

Point A :

From P, move 2 unit right and 2 unit up. So, A(2, 2).

Point B :

From P, move 2 unit right and 1 unit up. So, B(2, 1)

Point C :

From P, 5 unit right and 1 unit up. So, C(5, 1)

Point D :

From P, 5 unit right and 2 unit up. So, D(5, 2)

Rule for 180° rotation

(x, y) ==> (-x, -y)

A(2, 2)

B(2, 1)

C(5, 1)

D(5, 2)

A'(-2, -2)

B'(-2, -1)

C'(-5, -1)

D'(-5, -2)

Problem 2 :

Solution:

Point A:

From P, move 3 units left and 2 units down. So, A(-3, -2)

Point B:

From P, move 1 unit left and 2 units down. So, B(-1, -2)

Point C:

From P, move 1 unit left and 5 units down. So, C(-1, -5)

Rule for 90° clockwise rotation

(x, y) ==> (y, -x)

A(-3, -2)

B(-1, -2)

C(-1, -5)

A'(-2, 3)

B'(-2, 1)

C'(-5, 1)

Problem 3 :

Solution:

Point A:

From P, move 1 unit right and no vertical move. So, A(1, 0)

Point B:

From P, move 3 units right and 2 units down. So, B(3, 2)

Point C:

From P, move 5 units right and no vertical move. So, C(5, 0)

Rule for 90° anticlockwise rotation

(x, y) ==> (-y, x)

A(1, 0)

B(3, 2)

C(5, 0)

A'(0, 1)

B'(-2, 3)

C'(0, 5)

Problem 4 :

Solution:

Point A:

From P, move 4 units left and no vertical move. So, A(-1, 0)

Point B:

From P, move 1 unit left and 4 units down. So, B(-1, -4)

Point C:

From P, move 6 units right and 4 units down. So, C(6, -4)

Point D:

From P, move 6 units right and no vertical move. So, D(6, 0)

Rule for 90° clockwise rotation

(x, y) ==> (y, -x)

A(-1, 0)

B(-1, -4)

C(6, -4)

D(6, 0)

A'(0, 1)

B'(-4, 1)

C'(-4, -6)

D'(0, -6)

Problem 5 :

Solution:

Point A:

From P, move 5 units left and 4 units down. So, A(-5, -4)

Point B:

From P, move 3 units left and 3 units down. So, B(-3, -3)

Point C:

From P, move 3 units left and 6 units down. So, C(-3, -6)

Rule for 90° clockwise rotation

(x, y) ==> (y, -x)

A(-5, -4)

B(-3, -3)

C(-3, -6)

A'(-4, 5)

B'(-3, 3)

C'(-6, 3)

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EXAMPLES OF ROTATION OF 2D SHAPES WHEN CENTER OF ROTATION IS GIVEN

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