Question

If $T :(0,0) \rightarrow(5,1),$ then $T :(3,3) \rightarrow(?, ?)$

   If $T :(0,0) \rightarrow(5,1),$ then $T :(3,3) \rightarrow(?, ?)$

Geometry

Ray C.… 1st Edition

Chapter 14, Problem 3

Instant Answer

Solved by Expert Amrita Bhasin

10/27/2019

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This implies that the transformation adds 5 to the x-coordinate and 1 to the y-coordinate. Show more…

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If $T :(0,0) \rightarrow(5,1),$ then $T :(3,3) \rightarrow(?, ?)$

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Key Concepts

Translation

A translation is a geometric operation that shifts every point of a figure or space by the same fixed distance in a given direction. In coordinate geometry, this means adding a constant vector to the coordinates of every point, effectively relocating the entire figure without any rotation or change in shape.

Affine Transformation

An affine transformation is a function that maps points using a linear transformation followed by a translation. It preserves points, straight lines, and planes. In cases where the linear part is the identity, the affine transformation reduces to a simple translation, meaning every point is moved by the same fixed vector.

Vector Addition

Vector addition in the context of translations refers to the process of adding a fixed vector to the coordinates of a point. This operation shifts the point’s location by combining the coordinates of the original point with the components of the translation vector.

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