Translation and rotation are two fundamental transformations in geometry that can be applied to shapes or objects in a plane or space.
▎Translation
Definition: Translation involves moving every point of a shape or object a certain distance in a specified direction without changing its orientation or size.
Key Features:
• Direction and Distance: Each point of the object moves the same distance in the same direction.
• Preservation of Shape: The shape, size, and orientation remain unchanged.
• Vector Representation: Translations can be represented using vectors. For example, translating a point (x, y) by a vector (a, b) results in the new point (x + a, y + b) .
▎Rotation
Definition: Rotation involves turning a shape or object around a fixed point, known as the center of rotation, by a certain angle.
Key Features:
• Center of Rotation: The point around which the object rotates can be inside or outside the object.
• Angle of Rotation: The amount of turning is specified by an angle (measured in degrees or radians).
• Preservation of Shape: Like translation, rotation preserves the shape and size of the object. However, the orientation changes.
• Mathematical Representation: For a point (x, y) rotated around the origin by an angle θ , the new coordinates can be calculated using:
x' = x cos(θ) - y sin(θ)
y' = x sin(θ) + y cos(θ)
▎Summary
• Translation moves objects without altering their shape or orientation.
• Rotation changes the orientation of objects while keeping their shape and size intact.
Both transformations are essential in various fields such as computer graphics, robotics, and physics, allowing for the manipulation and analysis of geometric figures.
React godhaamee❤❤❤❤
Join now ➩ @daboo_academy
Join now ➩ @daboo_academy
For video Lectures check our youtube channel 👇👇👇👇👇👇👇
https://youtube.com/@DABOOACADAMY-e5k
▎Translation
Definition: Translation involves moving every point of a shape or object a certain distance in a specified direction without changing its orientation or size.
Key Features:
• Direction and Distance: Each point of the object moves the same distance in the same direction.
• Preservation of Shape: The shape, size, and orientation remain unchanged.
• Vector Representation: Translations can be represented using vectors. For example, translating a point (x, y) by a vector (a, b) results in the new point (x + a, y + b) .
▎Rotation
Definition: Rotation involves turning a shape or object around a fixed point, known as the center of rotation, by a certain angle.
Key Features:
• Center of Rotation: The point around which the object rotates can be inside or outside the object.
• Angle of Rotation: The amount of turning is specified by an angle (measured in degrees or radians).
• Preservation of Shape: Like translation, rotation preserves the shape and size of the object. However, the orientation changes.
• Mathematical Representation: For a point (x, y) rotated around the origin by an angle θ , the new coordinates can be calculated using:
x' = x cos(θ) - y sin(θ)
y' = x sin(θ) + y cos(θ)
▎Summary
• Translation moves objects without altering their shape or orientation.
• Rotation changes the orientation of objects while keeping their shape and size intact.
Both transformations are essential in various fields such as computer graphics, robotics, and physics, allowing for the manipulation and analysis of geometric figures.
React godhaamee❤❤❤❤
Join now ➩ @daboo_academy
Join now ➩ @daboo_academy
For video Lectures check our youtube channel 👇👇👇👇👇👇👇
https://youtube.com/@DABOOACADAMY-e5k