Find the distance between the point R( 2a+3, 8) and the point P(2a, 4).

Given the points R(2a+3, 8) and the point P(2a,
4).

We need to determine the distance between the point P
and the point R. Or we need to find the length of the segment
RP.

We will use the distance formula to find the
length.

We know that:

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

Let us
substitute.

==> D (RP) = sqrt[( 2a+3 - 2a)^2 + (
8-4)^2]

Reduce similar
terms.

==> D ( RP ) = sqrt( 3^2) + 4^2)
]

                    = sqrt( 9 +
16)

                   = sqrt( 25) =
5

Then, the distance between the point R(
2a+3, 8) and the point P(2a, 4) is 5 units.