Learn about the rules for 90 degree clockwise rotation aboutthe origin.
Howdo you rotate a figure 90 degrees in clockwise direction on a graph?
Rotation of point through 90° about the originin clockwise direction when point M (h, k) is rotated about the origin Othrough 90° in clockwise direction. The new position of point M (h, k) willbecome M’ (k, -h).
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Worked-out examples on 90 degree clockwise rotation about the origin:
1. Plot the pointM (-2, 3) on the graph paper and rotate it through 90° in clockwise direction,about the origin. Find the new position of M.
Solution:
When the point is rotated through 90° clockwise about theorigin, the point M (h, k) takes the image M' (k, -h).
Therefore, the new position of point M (-2, 3) will become M'(3, 2).
2. Find theco-ordinates of the points obtained on rotating the point given below through90° about the origin in clockwise direction.
(i) P (5, 7)
(ii) Q (-4, -7)
(iii) R (-7, 5)
(iv) S (2, -5)
Solution:
When rotated through 90° about the origin in clockwisedirection, the new position of the above points are;
(i) The new position of point P (5, 7) will become P' (7,-5)
(ii) The new position of point Q (-4, -7) will become Q'(-7, 4)
(iii) The new position of point R (-7, 5) will become R' (5,7)
(iv) The new position of point S (2, -5) will become S' (-5,-2)
3. Construct the image of the given figure under the rotation of 90° clockwise about the origin O.
Solution:
We get rectangular PQRS by plotting the points P (-3, 1), Q (3,1), R (3, -1), S (-3, -1). When rotatedthrough 90°, P' (1, 3), Q' (1, -3), R' (-1, -3) and S' (-1, 3).
Now join P'Q'R'S'.
Therefore, P'Q'R'S' is the new position of PQRS when it isrotated through 90°.
4. Draw a quadrilateralPQRS joining the points P (0, 2), Q (2, -1), R (-1, -2) and S (-2, 1) on thegraph paper. Find the new position when the quadrilateral is rotated through90° clockwise about the origin.
Solution:
Plot the point P (0, 2), Q (2, -1), R (-1, -2) and S (-2, 1)on the graph paper. Now join PQ, QR, RS and SP to get a quadrilateral. Onrotating it through 90° about the origin in clockwise direction, the newpositions of the points are
The new position of point P (0, 2) will become P' (2, 0)
The new position of point Q (2, -1) will become Q' (-1, -2)
The new position of point R (-1, -2) will become R' (-2, 1)
The new position of point S (-2, 1) will become S' (1, 2)
Thus, the new position of quadrilateral PQRS is P'Q'R'S'.
●Related Concepts
● Lines of Symmetry
● Point Symmetry
● Rotational Symmetry
● Order of Rotational Symmetry
● Types of Symmetry
● Reflection
● Reflection of a Point in x-axis
● Reflection of a Point in y-axis
● Reflection of a point in origin
● Rotation
● 90 Degree Clockwise Rotation
● 90 Degree Anticlockwise Rotation
● 180 Degree Rotation
7th Grade Math Problems
8th Grade Math Practice From 90 Degree Clockwise Rotation to HOME PAGE New! CommentsHave your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.
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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.
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)
Photostitcher 2 1 2 90 Degrees
Step 4 :
Vertices of the rotated figure are
![]()
P'(-3, 1), Q'(-4, -3), R'(0, -4) and S'(-1, 0)
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 :
Photostitcher 2 1 2 90 Degrees Celsius
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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