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 ABCABC is rotated about point PP, transforming it into triangle ABCA'B'C'.

  • The rotation from triangle ABCABC to triangle ABCA'B'C' is counterclockwise, since the new position of the triangle is turning left around point PP.
  • The angle of rotation can be determined by examining the direction of the triangles' vertices before and after rotation. Since AAA \to A', BBB \to B', and CCC \to C', it appears that the rotation is 9090^\circ counterclockwise.

For the clockwise direction, recall that a clockwise rotation is written with a negative degree. Therefore, the equivalent clockwise rotation would be 270-270^\circ.

Thus, the blanks can be filled in as:

  • 9090^\circ counterclockwise about PP
  • 270-270^\circ clockwise about PP

Would you like more details or have any further questions?

Here are 5 follow-up questions to expand on this concept:

  1. How do you determine the angle of rotation between two positions of a figure?
  2. What is the relationship between clockwise and counterclockwise rotations in degrees?
  3. Can a rotation be described in more than two ways?
  4. How would you verify if a rotation is correct using coordinates?
  5. What happens to the orientation of a shape when rotated by 180180^\circ?

Tip: Always pay attention to the direction of rotation. Clockwise is negative, and counterclockwise is positive when measuring angles of rotation.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Rotations
Angles

Formulas

Counterclockwise rotation angle
Clockwise rotation angle

Theorems

Rotation theorem

Suitable Grade Level

Grades 8-10