Graph each figure in the coordinate plane. Find the perimeter

Question

A(-4, -1), B(4,5),C(4,-2)

These are the coordinates 

 

Thank You. 

Answer 1

The length of the perimeter is the total length of all three sides added together. Therefore, we must find the lengths of AB, AC and BC. Remembering the distance formula is the square root of (x₂-x₁)² + (y₂-y₁)² we can the distance for each length:

AB:  √(4-(-4))²+(5-(-1))² = √(8)²+(6)² = √(64+36) = √100 = 10

AC:  √(4-(-4))²+(-2-(-1))² = √(8)²+(-1)² = √(64+1) = √65

BC:  √(4-4)²+(-2-5)² = √(0)²+(-7)² = √49 = 7

The perimeter is 10 + √65 + 7 = 17 + √65 ≅ 25.06.

Answer 2

We don't have graphing capabilities. But just use the distance formula to find the perimeter.

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

 

AB = √[(4 + 4)² + (5 + 1)²]

AB = √(8² + 6²) = √(64 + 36) = √ 100

AB = 10

 

BC = √[(4 - 4)² + (-2 - 5)²]

BC = √[(0)² + (-7)²)]= √49

BC = 7

 

AC = √[(4 + 4)² + (-2 + 1)²]

AC = √[8² + (-1)²] = √65

AC = √65

 

P = AB + BC + AC

P = 10 + 7 +√65

P = 17 + 8.062257

P ≈  25.1