(a)
To find: The number of fixed points of rotation
(a)
Answer to Problem 30WE
The number of fixed points of rotation
Explanation of Solution
Given information: It is given that a point P is known as fixed point of transformation T if
Calculation:
Consider the rotation
The rotation
Consider the reflection
All the x- coordinates of the line along the y -axis map to itself. So,
So, reflection
The dilation
(1) If
(2) If
(3) The center
For
For the dilation
So, the given dilation has only one fixed point.
Consider the translation
Each point for this transformation will map to every other point. No point maps to itself. So, there is no fixed point for this translation.
Therefore, the number of fixed points of rotation
(b)
To find: The coordinates of the fixed point of the composite
(b)
Answer to Problem 30WE
The coordinates of the fixed point of the composite
Explanation of Solution
Given information: The coordinates of point A is
Calculation:
The dilation of origin with scale factor 2 is:
The dilation of point A with scale factor
The coordinates of fixed point of composite
So, the fixed point is the origin.
Therefore, the coordinates of the fixed point of the composite
Chapter 14 Solutions
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