The give coordinates are (10, a), (1, 6) and distance d = .

The distance d between any two points with coordinates .

Then distance (d).

Substitute , and d = . \ \

Square each side and eliminate the square roots.

Evaluate powers: .

Apply subtraction property of equality: If a = b then .

Subtract 81 from each side.

Apply additive inverse property: .

Apply square roots property: If then .

Evaluate square roots:

Separate the solutions .

The first solution .

Apply addition property of equality: If a = b then a + b = b + a.

Add 6 to each side.

Apply additive inverse property: .

Multiply each side by negative one.

The second solution .

Apply addition property of equality: If a = b then a + b = b + a.

Add 6 to each side.

Apply additive inverse property: .

The value of a is 2 or 14.