   Chapter 15.9, Problem 12E

Chapter
Section
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 (0,0),(4,3),(2,4) and (2,1) .

Calculation:

Obtain the line by using line equation xx1x2x1=yy1y2y1 .

Compute the equation of the line that passes through the vertices (0,0) and (4,3) .

x040=y030x4=y33x=4y3x4y=0

Thus, the equation of the line that passes through the vertices (0,0) and (4,3) is 3x4y=0 .

Compute the equation of the line that passes through the vertices (4,3) and (2,4) .

x424=y343x42=y311(x4)=2(y3)

Simplify further as follows,

x4=2y+6x+2y=6+4x+2y=10

Thus, the equation of the line that passes through the vertices (4,3) and (2,4) is x+2y=10 .

Compute the equation of the line that passes through the vertices (2,4) and (2,1)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Show that limn(1+xn)n=exfor any x 0.

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 2340, find the indicated limit. 29. limt1(2x33x2+x+2)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

3. If what is

Mathematical Applications for the Management, Life, and Social Sciences

13. Write the formula for the mean of grouped data. (21-10)

Contemporary Mathematics for Business & Consumers

True or False: converges absolutely.

Study Guide for Stewart's Multivariable Calculus, 8th 