   Chapter 7.1, Problem 21E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 11 to 22, sketch and describe each locus in the plane.A city park is rectangular with dimensions of 800 feet by 1200 feet. A memorial is to be placed in the park, but is not to be built (placed) closer than 200 feet from a park boundary. Describe the locus of points characterized by possible locations of the memorial.

To determine

To find:

The locus of points characterized by possible locations of the memorial to be constructed in the city park of rectangular in shape with dimensions of 800 feet by 1200 feet and the memorial is not to be built (placed) closer than 200 feet from a park boundary.

Explanation

A locus is set of all points and only those points that satisfy a given condition or set of conditions.

In must be noted that, the phrase “all points and only those points” has dual meaning as follows:

1. All points of the locus satisfy the given condition.

2. All points satisfying the given locus conditions are included in the locus.

Calculation:

Step 1: Construct a rectangle ABCD of dimension BC=AD=800 feet by AB=CD=1200 feet.

Step 2: It is given that the memorial is to be constructed in the city park not closer than 200 feet from a park boundary.

Step 3: Locate the points 1 and 2 at a distance of 200 feet towards right and top from the point A respectively.

Step 4: Draw a vertical line and horizontal line from the points 1 and 2 respectively to locate the point E

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