Question

Computer Graphics Refer to Problem 97. The points $(-3,0),(-1,-2),(3,1)$, and $(1,3)$ are the vertices of a parallelogram $A B C D$. (a) Find the new vertices of a parallelogram $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ if it is translated by $\mathbf{v}=\langle 3,-2\rangle$. (b) Find the new vertices of a parallelogram $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ if it is translated by $-\frac{1}{2} \mathbf{v}$.

Name: Problem 98, Chapter 8: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2022-09-06T21:01:41-08:00
Duration: 2 min 37 s
Channel: Sheryl Ezze
Description: Computer Graphics Refer to Problem 97. The points (-3,0),(-1,-2),(3,1), and (1,3) are the vertices of a parallelogram A B C D. (a) Find the new vertices of a parallelogram A^' B^' C^' D^' if it is translated by 𝐯=⟨3,-2⟩. (b) Find the new vertices of a parallelogram A^' B^' C^' D^' if it is translated by -(1)/(2) 𝐯.

    Computer Graphics Refer to Problem 97. The points $(-3,0),(-1,-2),(3,1)$, and $(1,3)$ are the vertices of a parallelogram $A B C D$.
(a) Find the new vertices of a parallelogram $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ if it is translated by $\mathbf{v}=\langle 3,-2\rangle$.
(b) Find the new vertices of a parallelogram $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ if it is translated by $-\frac{1}{2} \mathbf{v}$.

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 98

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Solved by Expert Sheryl Ezze

09/06/2022

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Computer Graphics Refer to Problem 97. The points $(-3,0),(-1,-2),(3,1)$, and $(1,3)$ are the vertices of a parallelogram $A B C D$. (a) Find the new vertices of a parallelogram $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ if it is translated by $\mathbf{v}=\langle 3,-2\rangle$. (b) Find the new vertices of a parallelogram $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ if it is translated by $-\frac{1}{2} \mathbf{v}$.

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Key Concepts

Vector Addition

Vector addition is the process of adding two or more vectors together by summing their corresponding components. This concept is essential in executing translations, as each point in the object is moved by adding the translation vector to its original coordinates.

Translation

Translation is a geometric transformation that shifts every point of an object by the same vector, thereby producing a congruent object in a different location. In computer graphics, this operation involves adding a specific displacement vector to each coordinate of the shape, which preserves the shape's size, orientation, and overall structure.

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