Determine m∈R, such as the distance between the points A(2,m) and B(m,−2) is 4.

We'll recall the distance
formula:

d = sqrt[(xB - xA)^2 + (yB -
yA)^2]

Since the coordinates of A and B are given, we'll
replace them into the formula:

d = sqrt[(m-2)^2 +
(m+2)^2]

We'll expand the
binomials:

d = sqrt(m^2 - 4m + 4 + m^2 + 4m +
4)

d = sqrt(2m^2 + 8)

But d =
4 => sqrt(2m^2 + 8) = 4

We'll raise to square both
sides:

2m^2 + 8 = 16

2m^2 = 16
- 8

2m^2 = 8

m^2 =
4

m1 = -2 and m2 = 2

The real
values of m, such as the distance between the points A(2,m) and B(m,−2) to be 4, are:
{-2 ; 2}.