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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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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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