Reflection is a transformation process in which a figure is flipped over a line, known as the axis of reflection, to produce a mirror image. This section explores the concept of reflection in the coordinate plane, particularly focusing on reflections over the line and the line .
![Reflections](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fca5b423c-138a-4a12-8e23-d180d8013498-file.png&w=1200&q=75)
Reflection Over the Line y = x
Reflecting a point or shape over the line involves swapping the and coordinates of each point in the shape. This operation creates a mirror image across the line .
Key Concepts
- Axis of reflection: The line .
- Transformation rule: For a point , the reflected point .
![Reflection Over the Line y = x](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F7b6ec68d-c2b0-4659-8688-8804dcbf6b21-file.png&w=1080&q=75)
Image courtesy of BYJUS
Example 1: Reflecting a Single Point
Given a point , find its reflection over the line .
- Original coordinates: =
- Reflected coordinates: =
![Reflecting a Single Point](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fe80da86c-3e3a-491a-8a3b-fa9457d75d2b-file.png&w=828&q=75)
Example 2: Reflecting a Shape
Reflect triangle ABC with vertices at , , and over the line .
- Original vertices:
- Reflected vertices:
![Reflecting a Shape](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F1c2464fe-d27f-4f90-9f4d-6b65f0ae803e-file.png&w=1080&q=75)
Reflection Over the Line x = 3
When reflecting a shape over the line , the formula for the reflected point is used. This formula adjusts the x-coordinate based on its original distance from the line , while the y-coordinate remains unchanged.
Key Concepts
- Axis of reflection: The line .
- Transformation rule: For any point , the reflected point is .
Example 3: Reflecting a Single Point
Consider a point . Find its reflection over .
- Original coordinates:=
- Apply reflection formula:
![Reflecting a Single Point](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fcc883ccd-05a8-4eed-b206-9750705ebb2c-file.png&w=750&q=75)
Example 4: Reflecting a Rectangle
Reflect a rectangle with vertices at , , , and over .
- Original vertices:
- , , ,
- Reflected vertices using :
- , , ,
![Reflection](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Fc7cf973d-da13-4130-b431-e9e3bdd4b1a0-file.png&w=1920&q=75)