   Chapter 7.1, Problem 48E 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 39 and 42, refer to the line segments shown.Verify this theorem:The locus of points equidistant from two fixed points is the perpendicular bisector of the line segment joining those points.

To determine

To verify:

The locus theorem which states that the locus of points equidistant from two fixed points is the perpendicular bisector of the line segment joining those points.

Explanation

Theorem:

Locus Theorem:

The locus of points equidistant from two fixed points is the perpendicular bisector of the line segment joining those points.

Calculation:

Consider a line XY obtained by joining two fixed points X and Y as shown in figure.

To verify the locus theorem, follow the below procedure:

1. Take X as center and any length greater than XY draw an arc above the line XY.

2. Take Y as center and draw an arc above the line XY.

3. Name the intersection point as Z.

4. Draw a line perpendicular to the line XY and through the point Z. This line bisects the line XY.

From the figure, we find that

XB=BZ

AX=AZ

AXB=AZB

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