Math Problem Statement
FILL IN THE BLANKS!
A triangle is rotated about point P. Complete the sentence to accurately describe the degree of rotation in both directions.
Solution
From the image, we see that triangle is rotated about point , transforming it into triangle .
- The rotation from triangle to triangle is counterclockwise, since the new position of the triangle is turning left around point .
- The angle of rotation can be determined by examining the direction of the triangles' vertices before and after rotation. Since , , and , it appears that the rotation is counterclockwise.
For the clockwise direction, recall that a clockwise rotation is written with a negative degree. Therefore, the equivalent clockwise rotation would be .
Thus, the blanks can be filled in as:
- counterclockwise about
- clockwise about
Would you like more details or have any further questions?
Here are 5 follow-up questions to expand on this concept:
- How do you determine the angle of rotation between two positions of a figure?
- What is the relationship between clockwise and counterclockwise rotations in degrees?
- Can a rotation be described in more than two ways?
- How would you verify if a rotation is correct using coordinates?
- What happens to the orientation of a shape when rotated by ?
Tip: Always pay attention to the direction of rotation. Clockwise is negative, and counterclockwise is positive when measuring angles of rotation.
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Math Problem Analysis
Mathematical Concepts
Geometry
Rotations
Angles
Formulas
Counterclockwise rotation angle
Clockwise rotation angle
Theorems
Rotation theorem
Suitable Grade Level
Grades 8-10