Show that the points (6, 5) and (5, 6) are the same distance from the origin. The distance from the point (6, 5) to the origin is        . The distance from the point (5, 6) to the origin is        . (b) Show that the points (a, b) and (b, a) are the same distance from the origin. The distance from the point (a, b) to the origin is        . The distance from the point (b, a) to the origin is

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 31E
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(a) Show that the points (6, 5) and (5, 6) are the same distance from the origin.

The distance from the point (6, 5) to the origin is
 
 
 
 .
The distance from the point (5, 6) to the origin is
 
 
 
 .


(b) Show that the points (ab) and (ba) are the same distance from the origin.

The distance from the point (a, b) to the origin is
 
 
 
 .
The distance from the point (b, a) to the origin is
Expert Solution
Step 1

Let point A= (6,5) and point B=(5,6)

Distance between two points x1,y1 and x2,y2 is calculated as

AB = x2-x12+y2-y12

We have to show that point A and point B are at the same distance from the origin 

 

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