Find a if the distance between (6.2) and (0,a) is 10 units

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Given the distance between the points (0, 6) and ( 2,a) is 10 units.

We will use the distance between two points formula to solve.

We know that:

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

Then, we will substitute.

==> D = sqrt( 6-0)^2 + ( a-2)^2 = 10

==> sqrt(6^2) +(a-2)^2 = 10

==> sqrt(36+(a-2)^2] = 10

Now we will square both sides.

==> 36 + (a-2)^2 = 100.

Now we will subtract 36 from both sides.

==> (a-2)^2 = 64.

Now we will take the root of both sides.

==> (a-2) = +- 8

==> (a-2) = 8 ==> a= 10

==> (a-2) = -8 ==> a= -6

Then we have two possible values for a.

==> a1= 10

==> a2= -6

**Then, the points ( 0, -6) and ( 0, 10) are located 10 units from the point (6,2).**

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