distance between points

Question

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

(2,-√2)(r,√2)

Answer 1

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.

Answer 2

Given two points are

Formula fore distance between two points is

Substitute values

r = 2 + 2

r = 4

Comments

The values of  r is 0 and 4.