BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.8, Problem 19E
To determine

To calculate: The area of the rectangle with vertices A(1,3),B(5,3),C(1,3) and D(5,3) and also plot the vertices on the coordinate plane.

Expert Solution

Answer to Problem 19E

The area of the rectangle is 24 sq units . The rectangle so formed is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 19E , additional homework tip  1

Explanation of Solution

Given information:

The vertices of rectangle A(1,3),B(5,3),C(1,3) and D(5,3) .

Formula used:

Distance d(A,B) between two points A=(x1,y1) and B=(x2,y2) in the Cartesian plane is denoted by d(A,B)=(x2x1)2+(y2y1)2 .

Area of rectangle is l×b where l is the length and b is the breadth of the rectangle.

Calculation:

Consider the vertices of rectangle A(1,3),B(5,3),C(1,3) and D(5,3) .

Toplot the points A(1,3),B(5,3),C(1,3) and D(5,3) in the coordinate plane.

Construct a Cartesian plane with vertical axis as y-axis and horizontal axis as x-axis.

Marks the numbers on both the axes.

Plot the points A(1,3),B(5,3),C(1,3) and D(5,3) .

And join them to form a rectangle.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 19E , additional homework tip  2

Recall that area of rectangle is l×b where l is the length and b is the breadth of the rectangle.

Evaluate the length and breadth of the rectangle obtained above.

Recall that the distance d(A,B) between two points A=(x1,y1) and B=(x2,y2) in the Cartesian plane is denoted by d(A,B)=(x2x1)2+(y2y1)2 .

Evaluate the distance between A(1,3) and B(5,3) .

  d(A,B)=(51)2+(33)2=16=4

Evaluate the distance between A(1,3) and C(1,3) .

  d(A,C)=(11)2+(33)2=36=6

Therefore, length is 6 and breadth is 4 units.

Now, area of rectangle is,

  l×b=6×4=24

Thus, the area of the rectangle is 24 sq units .

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