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distance between points

0 votes

Distance between two points is 2√3 units;find r

(2,-√2)(r,√2)

asked Oct 31, 2013 in GEOMETRY by payton Apprentice

2 Answers

0 votes

distance between points

Lets

A(x1,y1) = (2,-√2)

B(x2,y2) = (r,√2)

Distance between two points is

d = √(x2-x1)2+(y2-y1)2

d = √(r-2)2+(√2-(-√2)2

d = √(r-2)2+(√2+√2)2

d = √(r-2)2+(2√2)2

d = √r2-4r+4+(2)2(√2)2

d = √r2-4r+12

The given problem distance between the two points is 2√3

√r2-4r+12 = 2√3

Take squares on each side

(√r2-4r+12)2 = (2√3)2

Cancel squares and roots

r2-4r+12 = 12

Subtract 12 from each side

r2-4r+12-12 = 12-12

r2-4r = 0

Common same terms

r(r-4) = 0

r=0 or r-4 = 0                       (By the zero product property)

r-4 = 0

Add 4 to each side

r-4+4 = 0+4

r = 4

The values of  \"r\" is 0 and  4.

answered Oct 31, 2013 by rob Pupil
0 votes

Given two points are

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Formula fore distance between two points is

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Substitute values

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r = 2 + 2

r = 4

answered Oct 31, 2013 by jouis Apprentice

The values of  r is 0 and 4.

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