   Chapter 10.1, Problem 27E 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

Use the method of Example 4 to find the equation of the line that describes all points equidistant from the points ( 1 ,   2 ) and ( 4 ,   5 ) .

To determine

To find:

The equation of the line that describes all points equidistant from the points (1, 2) and (4, 5).

Explanation

Given points are,

(1, 2) and (4, 5).

Sketch the given coordinates in the graph and draw a line as shown in the figure.

The locus of the points equidistance from two fixed points is a line.

In the graph, MX is the line which is perpendicular bisector of AB-.

If X is on the locus, then AX=BX.

Let the coordinates of X=(x,y)

AX=BX

(x-1)2+(y-2)2=(x-4)2+(y-5)2

(x-1)2+(y-2)2=(x-4)2+(y-5)2

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