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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