The value of a in the given coordinates is 2.25.
Length of the lines joining the points
Apply Pythagoras theorem to determine the length of the lines.
|AC|² = |AB|² + |BC|²
(1 - 3)² + (10 - a)² = (3 - 3)² + (2 - a)² + (1 - 3)² + (10 - 2)²
4 + 100 - 20a + a² = 4 - 4a + a² + 4 + 64
104 - 20a + a² = 68 - 4a + a²
104 - 20a = 68 - 4a
104 - 68 = 20a - 4a
36 = 16a
a = 36/16
a = 2.25
Thus, the value of a in the given coordinates is 2.25.
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