Find the Perimeter of ABC. A(-2, 2) B(5, -3) C(-4, -1)

Question

Find the Perimeter of ΔABC. A(-2,2) B(5,-3) C(-4,-1)

Answer 1

Hi Daniel,

 

Because we don't know the lengths of ABC's sides, we can use the distance formula to find the distance, or length, of each side. Remember the distance formula is: d = √[(x2 - x1)^2 + (y2 - y1)^2].

 

AB, where A is (x1, y1) and B is (x2, y2):

   d = √[(5 - (-2))^2 + (-3 - 2)^2]

   d = √[7^2 + (-5)^2]

   d = √[49 + 25] = √[74] ≈ 8.602

 

BC, where B is (x1. y1) and C is (x2. y2):

   d = √[(-4 - 5)^2 + (-1 - (-3))^2]
   d = √[(-9)^2 + 2^2]
   d = √[81 + 4] = √[85] ≈ 9.220

 

CA, where C is (x1, y1) and A is (x2, y2):

   d = √[(-2 - (-4))^2 + (2 - (-1))^2]
   d = √[2^2 + 3^2]
   d = √[4 + 9] = √[13] ≈ 3.606

 

To find the perimeter, we can add the three sides together, using their most accurate representations:

 

√[74] + √[85] + √[13] ≈ 21.43

 

Hope this helps!