9514 1404 393
Answer:
about 106.5 units
Explanation:
The length of each side is found using the distance formula:
d = √((x2-x1)^2 +(y2-y1)^2)
For example, the length of side AB is ...
d = √((9 -2)^2 +(1 -3)^2) = √(7^2 +(-2)^2) = √53 ≈ 7.28
The other side lengths are calculated the same way. The sum of side lengths of the given triangle is ...
AB +BC +CA = 7.28 +13.34 +14.87 = 35.49
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Multiplying each coordinate by 3 effectively dilates the triangle by a factor of 3 about the origin. That increases the perimeter by a factor of 3, so it is ...
3(35.49) ≈ 106.5 . . . . units
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I find it convenient to use a calculator or spreadsheet to do the tedious calculations.