SECTION 7.7IDENTIFYING TYPES OF SYMMETRYON THE CARTESIAN PLANE
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TYPES OF SYMMETRY ON A CARTESIAN PLANE
There are several different types of symmetry:
Reflections:
Horizontal reflected over the Y-axis (side ways)
Vertical Reflected over the X-axis (Up/Down)
Diagonal Reflected over the line y = x (Up Right)
Rotations
Rotate an image about a point
Quarter Rotation – 90 degrees, Half Rotation – 180 degrees
CW – clockwise rotation, CCW – counter clockwise rotation
In this lesson, we will identify which symmetry isrequired to transform one object to another image
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EX: WHAT TYPE OF SYMMETRY IS REQUIRED TO TRANSFORM THEBLUE OBJECT TO THE RED IMAGE?
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
Would it be a reflection?
YES
Would it be a rotation?
Notice that all the dotted lines cross
at a point? This is the point of rotation
YES
Would it be a reflection?
YES
Would it be a rotation?
YES
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EX: WHICH OF THE FOLLOWING TRANSFORMATION WILLCHANGE THE OBJECT (BLUE) TO THE IMAGE (RED)
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
A)Reflection over the X-axis
B)Reflection over the Y-axis
C)180° rotation about the origin
D)90° CW rotation about the origin
E)90° CCW rotation about the origin
NO
YES
NO
YES
NO
Both answers B) and D) are correct
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INDICATE THE TYPE OF SYMMETRY FOR THEFOLLOWING TRANSFORMATION:
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
A)Reflection over the X-axis
B)Reflection over the Y-axis
C)Reflection over the line X = 1
D)90° CW rotation about the point (1, –1)
E)A translation of 6 units to the right
NO
NO
YES
NO
YES
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