The coordinates of the vertices of a triangle are A( 2,3) , B ( 9,1) , C ( 12,14) Suppose each coordinate is multiplied by 3. What is the perimeter of this triangle?

9514 1404 393

  about 106.5 units

Step-by-step 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.

Situation 1:

If water is pumped from the tank for use by the family, then the equation is:

Situation 2:

If the water is pumped from the water source in the tank to be stored in the tank, then the equation is: