Find a if the distance between A(a,3) and B( 4, a+3) is 4 units.

Given the points A(a,3)  B (4,
a+3)

Also, given that the distance between A and B is 4
units.

We will use the distance formula to
solve:

We know that:

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

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

==> sqrt( 16 - 8a + a^2 + a^2) =
4

==> sqrt( 2a^2 - 8a + 16) =
4

Square both sides:

==> 2a^2 -
8a + 16) = 16

==>  2a^2 - 8a =
0

==> 2a( a - 4) = 0

==>
a= 0   and a= 4

Then there are 2 possible
solutions:

a = { 0 ,
4}