Reflection and Rotation Formula Explained | Transformation | Class 10 Optional Mathematics Nepal

Описание: Welcome to Everest Online Academy! In this video, we explore Reflection and Rotation Formulas , key topics in the Class 10 Optional Mathematics syllabus under the chapter Transformation . Understanding how to apply these formulas to solve problems is crucial for scoring well in your SEE exams. Whether you're struggling with transformations or need help solving numerical problems step-by-step, this video will guide you with clear explanations and solved examples.

✅ What You’ll Learn in This Video:

Introduction to Transformation :
What is Transformation? (Definition and Types)
Types of Transformations:
Reflection: Flipping a shape over a line.
Rotation: Turning a shape around a point.
Translation: Moving a shape without changing its size or orientation.
Enlargement: Scaling a shape up or down from a center of enlargement.
Key Concepts :
Reflection :
Formula for Reflection:
Over the X-Axis:
(x,y)→(x,−y)
Over the Y-Axis:
(x,y)→(−x,y)
Over the Line y=x:
(x,y)→(y,x)
Over the Line y=−x:
(x,y)→(−y,−x)
Example: Reflecting the point (3,4) over the X-Axis results in (3,−4).
Rotation :
Formula for Rotation about the Origin:
90° Clockwise:
(x,y)→(y,−x)
90° Counterclockwise:
(x,y)→(−y,x)
180° Rotation:
(x,y)→(−x,−y)
Example: Rotating the point (2,3) 90° clockwise results in (3,−2).
Combined Transformations :
Steps:
Perform the first transformation (e.g., reflection).
Use the result as input for the second transformation (e.g., rotation).
Repeat for additional transformations if needed.
Matrix Representation of Transformations :
Reflection Matrices:
Over the X-Axis:
[
1
0
​

0
−1
​
]
Over the Y-Axis:
[
−1
0
​

0
1
​
]
Rotation Matrices:
90° Clockwise:
[
0
−1
​

1
0
​
]
90° Counterclockwise:
[
0
1
​

−1
0
​
]
180° Rotation:
[
−1
0
​

0
−1
​
]
Step-by-Step Solutions to SEE Past Year Questions :
Solving numerical problems involving Reflection and Rotation.
Application of concepts in real exam questions.
Common Mistakes to Avoid While Solving Transformation Problems
Tips to Score Full Marks in Transformation Questions
Practice Exercises for Better Understanding
💡 Why Watch This Video?
The Reflection and Rotation chapter is a frequently tested topic in the Class 10 Optional Mathematics exam, especially in the context of combined transformations and matrix calculations. By mastering these formulas, you can confidently tackle exam questions and secure full marks in this section. This video simplifies the theory, provides solved examples, and includes practical tips to ensure you’re fully prepared.

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💬 Let’s Discuss:
Have any doubts or questions about Reflection, Rotation, or related topics? Drop them in the comments below, and we’ll get back to you as soon as possible. Also, let us know what other topics or SEE questions you’d like us to cover in future videos.

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