   Chapter 7.1, Problem 18E 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

Note: Exercises preceded by an asterisk are of a more challenging nature.In Exercises 11 to 22, sketch and describe each locus in the plane.Find the locus of points in the interior of a right triangle with sides of 6 in., 8 in., and 10 in and at a distance of 1 in. from the triangle.

To determine

To find:

The locus of points in the interior of a right triangle with sides of 6 in., 8 in., and 10 in and at a distance of 1 in. from the triangle.

Explanation

Approach:

The locus of points in a plane that are equidistant from the endpoints of a line segment is the perpendicular bisector of that line segment.

Calculation:

Step 1: Construct a right triangle (shown in black) with sides of 6 in., 8 in., and 10 in.

Step 2: Construct another right triangle (shown in red) with an offset of 1 in. interior of the first triangle as shown in figure.

Thus, the locus of points in the interior of a right triangle with sides of 6 in., 8 in., and 10 in and at a distance of 1 in

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