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.
270° clockwise 270° counter clockwise 90° clockwise 90° counter clockwise |
(x, y) ==> (-y, x) (x, y) ==> (y, -x) (x, y) ==> (y, -x) (x, y) ==> (-y, x) |
Note :
90° clockwise and 270° counter clockwise both are same.
Rotate each shape as described.
Problem 1 :
The shape above has the following coordinates:
A (-2, 0), B (-7, 3) and C(-9, 7)
Rotate the shape 270° counter-clockwise.
Solution:
Here, triangle is rotated 270° counterclockwise. So, the rule that we have to apply here is
(x, y) ---> (y, -x)
A(-2, 0) = A'(0, 2)
B(-7, 3) = B'(3, 7)
C(-9, 7) = C'(7, 9)
Vertices of the rotated figure are
A'(0, 2), B'(3, 7) and C'(7, 9)
Problem 2 :
The shape above has the following coordinates:
A(4, 0), B(10, -1), C(8, -6) and D(3, -9)
Rotate the shape 270° counter-clockwise.
Solution:
Here, triangle is rotated 270° counterclockwise. So, the rule that we have to apply here is
(x, y) ---> (y, -x)
A(4, 0) = A'(0, -4)
B(10, -1) = B'(-1, -10)
C(8, -6) = C'(-6, -8)
D(3, -9) = D'(-9, -3)
Vertices of the rotated figure are
A'(0, -4), B'(-1, -10), C'(-6, -8) and D'(-9, -3)
Problem 3 :
The shape above has the following coordinates:
A (0, -1), B (-8, -4) and C (-10, -10)
Rotate the shape 90° counter-clockwise.
Solution:
Here, triangle is rotated 90° counterclockwise. So, the rule that we have to apply here is
(x, y) ---> (-y, x)
A(0, -1) = A'(1, 0)
B(-8, -4) = B'(4, -8)
C(-10, -10) = C'(10, -10)
Vertices of the rotated figure are
A'(1, 0), B'(4, -8) and C'(10, -10)
Problem 4 :
The shape above has the following coordinates:
A (0, 0), B (-9, -3), C(-8, -10) and D(-2, -6)
Rotate the shape 90° clockwise.
Solution:
Here, triangle is rotated 90° clockwise. So, the rule that we have to apply here is
(x, y) ---> (y, -x)
A(0, 0) = A'(0, 0)
B(-9, -3) = B'(-3, 9)
C(-8, -10) = C'(-10, 8)
D(-2, -6) = D'(-6, 2)
Vertices of the rotated figure are
A'(0, 0), B'(-3, 9), C'(-10, 8) and D'(-6, 2)
Rotate each shape as described.
Problem 5 :
The shape above has the following coordinates:
A (-3, 3), B (-7, 2) and C (-8, 6)
Rotate the shape 270° clockwise.
Solution:
Here, triangle is rotated 270° clockwise. So, the rule that we have to apply here is
(x, y) ---> (-y, x)
A(-3, 3) = A'(-3, -3)
B(-7, 2) = B'(-2, -7)
C(-8, 6) = C'(-6, -8)
Vertices of the rotated figure are
A'(-3, -3), B'(-2, -7) and C'(-6, -8)
Problem 6 :
The shape above has the following coordinates:
A (-4, -2), B (-9, 0), C (-6, -7) and D (-5, -8)
Rotate the shape 90° counter-clockwise.
Solution:
Here, triangle is rotated 90° counterclockwise. So, the rule that we have to apply here is
(x, y) ---> (-y, x)
A(-4, -2) = A'(2, -4)
B(-9, 0) = B'(0, -9)
C(-6, -7) = C'(7, -6)
D(-5, -8) = D'(8, -5)
Vertices of the rotated figure are
A'(2, -4), B'(0, -9), C'(7, -6) and D'(8, -5)
Problem 7 :
The shape above has the following coordinates:
A (-5, 3), B (-6, 1) and C (-9, 9)
Rotate the shape 270° clockwise.
Solution:
Here, triangle is rotated 270° clockwise. So, the rule that we have to apply here is
(x, y) ---> (-y, x)
A(-5, 3) = A'(-3, -5)
B(-6, 1) = B'(-1, -6)
C(-9, 9) = C'(-9, -9)
Vertices of the rotated figure are
A'(-3, -5), B'(-1, -6) and C'(-9, -9)
Problem 8 :
The shape above has the following coordinates:
A (-2, -1), B(-6, -3), C(-7, -6) and D(-1, -9)
Rotate the shape 270° clockwise.
Solution:
Here, triangle is rotated 270° clockwise. So, the rule that we have to apply here is
(x, y) ---> (-y, x)
A(-2, -1) = A'(1, -2)
B(-6, -3) = B'(3, -6)
C(-7, -6) = C'(6, -7)
D(-1, -9) = D'(9, -1)
Vertices of the rotated figure are
A'(1, -2), B'(3, -6), C'(6, -7) and D'(9, -1)
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