https://file.aiquickdraw.com/mathbot/file/1726519334395jv7rp4es.jpg

Draw the image of the rotation of quadrilateral \[SORT\] by \[270^\circ\] about the origin.


To rotate the quadrilateral \( SORT \) by \( 270^\circ \) counterclockwise about the origin, we follow these steps for each vertex of the quadrilateral. The formula for rotating a point \( (x, y) \) by \( 270^\circ \) counterclockwise around the origin is:

\[
(x', y') = (y, -x)
\]

Here are the steps for each point in quadrilateral \( SORT \):

1. **Point \( S(-2, -2) \)**: After rotation by \( 270^\circ \):
   \[
   S' = (-2, -(-2)) = (-2, 2)
   \]

2. **Point \( O(-2, 1) \)**: After rotation by \( 270^\circ \):
   \[
   O' = (1, 2)
   \]

3. **Point \( R(1, 3) \)**: After rotation by \( 270^\circ \):
   \[
   R' = (3, -1)
   \]

4. **Point \( T(5, 1) \)**: After rotation by \( 270^\circ \):
   \[
   T' = (1, -5)
   \]

Now that we have the coordinates of the rotated points, you can plot them on the grid to complete the quadrilateral. The new coordinates of the rotated quadrilateral \( S' O' R' T' \) are:

\[
S'(-2, 2), O'(1, 2), R'(3, -1), T'(1, -5)
\]

Would you like further assistance with plotting or visualizing this rotation?

Here are five related questions to consider:
1. How do you rotate a point by \( 90^\circ \) about the origin?
2. What is the effect of rotating a shape by \( 180^\circ \) around the origin?
3. What happens to the coordinates if you rotate by \( 360^\circ \)?
4. How does rotating by \( 270^\circ \) differ from rotating by \( -90^\circ \)?
5. How would the shape look if rotated by only \( 90^\circ \)?

**Tip:** When rotating shapes, always check the signs of the new coordinates to ensure the correct quadrant placement.

Draw the image of the rotation of quadrilateral SORT by 270° about the origin.

Learn how to rotate quadrilateral SORT by 270° about the origin using the transformation formula (x', y') = (y, -x). This problem explores key geometry concepts like rotation and transformation, ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation