Multiple Choice
Given the function , what are the values of the vertical shift and the phase shift ?
0. Review of College Algebra
Transformations
Multiple Choice
Given segment in the plane, what is the image of segment after a -degree clockwise rotation about point ?
A
Segment
B
Segment
C
Segment
D
Segment
Verified step by step guidance1
Identify the center of rotation, which is point \(H\), and note the angle of rotation is \(120\) degrees clockwise.
Recall that a rotation of \(\theta\) degrees clockwise about a point \(H\) can be represented by rotating each point of the segment around \(H\) by \(\theta\) degrees in the clockwise direction.
To find the image of segment \(BC\), rotate both endpoints \(B\) and \(C\) around \(H\) by \(120\) degrees clockwise. This involves calculating the new coordinates of \(B'\) and \(C'\) after rotation.
Use the rotation formulas for a point \((x,y)\) rotated about \((h,k)\) by \(\theta\) degrees clockwise:
\( x' = h + (x - h) \cos(\theta) + (y - k) \sin(\theta) \)
\( y' = k - (x - h) \sin(\theta) + (y - k) \cos(\theta) \)
where \(\theta = 120^\circ\).
After finding the coordinates of \(B'\) and \(C'\), connect these points to form the image segment \(B'C'\), which is the rotated image of segment \(BC\) about point \(H\).
Related Videos
Related Practice
