equation for transformations
(y-a)/c = f(x-b)/d
In mathematics, a transformation is a process that changes the position, shape, or size of an object. Transformations are commonly used in geometry and algebra to describe how a figure or function changes. The equation for transformations depends on the type of transformation being performed.
1. Translation:
A translation moves an object in a specific direction without changing its shape or orientation. The equation for a translation is given as:
(x, y) → (x + a, y + b)
Where (x, y) are the original coordinates, and (x + a, y + b) are the translated coordinates.
2. Reflection:
A reflection is a transformation that flips an object over a line of symmetry. The equation for reflection over the x-axis is given as:
(x, y) → (x, -y)
The equation for reflection over the y-axis is given as:
(x, y) → (-x, y)
3. Rotation:
A rotation is a transformation that turns an object about a point. The equation for rotation about the origin by an angle θ is given as:
(x, y) → (xcosθ – ysinθ, xsinθ + ycosθ)
Where x and y are the original coordinates and θ is the angle of rotation.
4. Dilation:
A dilation is a transformation that changes the size of an object. The equation for dilation by a scale factor k is given as:
(x, y) → (kx, ky)
Where x and y are the original coordinates and k is the scale factor. If k > 1, the dilation is an enlargement. If k < 1, the dilation is a reduction. These are the equations for some of the commonly used transformations in mathematics. By applying these equations, one can easily transform geometric figures and solve algebraic problems.
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