The give coordinates are (3, 1), (a, 7) and distance d = 10.

The distance d between any two points with coordinates .

Then distance (d).

  (Substitute , and d = 10)

        (Product of two same signs is positive)

              (Add: 7 + 1 = 8)

            (Square each side and eliminate the square roots)

Evaluate powers: .

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

   (Subtract 64 from each side)

                   (Apply additive inverse property: )

                             (Subtract: )

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 3 to each side)

                                 (Apply additive inverse property: )

                                       (Add: )

The second solution .

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

                         (Add 3 to each side)

                                     (Apply additive inverse property: )

                                           (Add: 6 + 3 = 9)

The value of a is 3 and 9.