Applying the Transformation to Point S

Oct 13, 2025 by miodeya.com 16 views

Introduction

In geometry, transformations are essential concepts that help us understand how shapes change under various operations. One common type of transformation is a rotation, which involves rotating a shape around a fixed point by a certain angle. In this article, we will explore a triangle transformation problem involving a rotation of 270 degrees. We will apply the transformation rule to find the coordinates of point S'.

The Original Triangle

The original triangle has vertices at points R(1,1), S(-2,-4), and T(-3,-3). To visualize the triangle, we can plot these points on a coordinate plane.

Original Triangle Coordinates

Point	x-coordinate	y-coordinate
R	1	1
S	-2	-4
T	-3	-3

The Transformation Rule

The triangle is transformed according to the rule R0, 270°. This means that the triangle is rotated 270 degrees around the origin (0,0). To apply this transformation, we need to understand how a 270-degree rotation affects the coordinates of a point.

Rotation of 270 Degrees

A 270-degree rotation is equivalent to a 90-degree counterclockwise rotation. When a point (x,y) is rotated 90 degrees counterclockwise, its new coordinates become (-y,x).

Applying the Transformation to Point S

To find the coordinates of S', we need to apply the transformation rule to point S(-2,-4). Using the rotation formula, we can calculate the new coordinates of S'.

New Coordinates of S'

Point	x-coordinate	y-coordinate
S	-2	-4
S'	-(-4)	-(-2)
S'	4	2

Conclusion

In this article, we applied a 270-degree rotation transformation to a triangle with vertices at points R(1,1), S(-2,-4), and T(-3,-3). We used the rotation formula to find the new coordinates of point S'. The final answer is S' = (4,2).

Discussion

This problem demonstrates the importance of understanding geometric transformations, particularly rotations. By applying the transformation rule, we can find the coordinates of a point after a rotation. This concept is essential in various fields, including engineering, physics, and computer graphics.

Introduction

In our previous article, we explored a triangle transformation problem involving a rotation of 270 degrees. We applied the transformation rule to find the coordinates of point S'. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the transformation rule R0, 270°?

A: The transformation rule R0, 270° means that the triangle is rotated 270 degrees around the origin (0,0).

Q: How does a 270-degree rotation affect the coordinates of a point?

A: A 270-degree rotation is equivalent to a 90-degree counterclockwise rotation. When a point (x,y) is rotated 90 degrees counterclockwise, its new coordinates become (-y,x).

Q: How do I apply the transformation rule to a point?

A: To apply the transformation rule, you need to use the rotation formula: (x',y') = (-y,x), where (x,y) are the original coordinates of the point.

Q: What are the new coordinates of point S after the transformation?

A: Using the rotation formula, we can calculate the new coordinates of S: S' = (4,2).

Q: Why is the final answer S' = (4,2) and not S' = (-4,2)?

A: The final answer S' = (4,2) is correct because the rotation formula (-y,x) is applied to the original coordinates of S (-2,-4). This results in the new coordinates (4,2).

Q: Can I apply the transformation rule to other points in the triangle?

A: Yes, you can apply the transformation rule to other points in the triangle. For example, you can find the new coordinates of point T by applying the rotation formula to its original coordinates.

Q: What is the importance of understanding geometric transformations?

A: Understanding geometric transformations is essential in various fields, including engineering, physics, and computer graphics. It helps you to analyze and solve problems involving shapes and their transformations.

Conclusion

In this article, we answered some frequently asked questions related to the triangle transformation problem. We hope that this Q&A article helps you to better understand the concept of geometric transformations and how to apply them to solve problems.