Step-by-step explanation:
To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x). Let's understand the rotation of 90 degrees clockwise about a point visually. ... Then we can join the points and find the new positioned figure.
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 :
Vertices of the rotated figure are
R'(-4, -2), S'(-4, -4), T'(-3, -5), U'(-2, -4) and E'(-2, -2)
