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

Question

points are (2,-√2)(r,√2), please help!

Answer 1

Find value of r:-

Given two points (2, -√2) (r, √2).

Distance between Given two points is 2√3.

Distance between (x1,y1) and (x2,y2) is sqrt (x2-x1)^2 + (y2-y1)^2

2√3 = sqrt (r - 2)^2 + (√2 - (-√2))^2

Squaring on each side

(2√3)^2 = (r - 2)^2 + (√2 - (-√2))^2

12 = (r - 2)^2 + (√2 - (-√2))^2

Product of two same signs is positive

12 = (r - 2)^2 + (√2 + √2)^2

12 = (r - 2)^2 + (2√2)^2

12 = (r - 2)^2 + 8

12 = (r)^2 + 4 - 4r + 8

12 = (r)^2  -  4r + 12

Subtract 12 from each side

12 - 12 = (r)^2  -  4r + 12 - 12

 0 = (r)^2  -  4r

0 = r(r - 4)

In the above equation either r = 0 or r = 4.

The value of r = 0 (or) r = 4.