Chapter 15.9, Problem 12E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A region *R* in the *xy*-plane is given. Find equations for a transformation *T* that maps a rectangular region *S* in the *uv*-plane onto *R*, where the sides of *S* are parallel to the *u-* and *v*-axes.

**12.** *R* is parallelogram with vertices (0, 0), (4, 3), (2, 4), (–2, 1)

To determine

**To find:** The equation for the transformation *T* maps with given rectangular region *S*.

Explanation

**Given:**

A region *R* is the parallelogram with vertices

**Calculation:**

Obtain the line by using line equation

Compute the equation of the line that passes through the vertices

Thus, the equation of the line that passes through the vertices

Compute the equation of the line that passes through the vertices

Simplify further as follows,

Thus, the equation of the line that passes through the vertices

Compute the equation of the line that passes through the vertices

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