A triangle's coordinates tell you its perimeter because they specify the exact positions of all three of its vertices. These positions determine the length of each side, and the triangle's perimeter is the sum of the three lengths. Calculate the length of each side using the Pythagorean theorem. The theorem states that the length of a diagonal, squared, equals the sum of the squares of the horizontal and vertical lines that the diagonal joins.

Subtract the first point's xcoordinate from that of the second. If, for instance, two of the triangle's points have coordinates of (1, 9) and (13, 12), you would calculate 13  1 = 12.

Square this difference  12^2 = 144.

Subtract the first point's ycoordinate from the second's: 12  9 = 21.

Square this difference. So (21)^2 = 441

Add together the two squares  144 + 441 = 585.

Find the square root of this sum  585^0.5 = 24.19. This side measures 24.19 units in length.

Repeat the whole process with the other two sides. If the third corner, for instance, has coordinates of (5, 6), the second side measures ((1  5)^2 + (9  6)^2 )^0.5, or 16.15 units. The third side measures ((13  5)^2 + (12  6)^2 ) ^ 0.5, or 18.97 units.

Add together the three measurements to find the perimeter  24.19 + 16.15 + 18.97 = 59.31 units.
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