Question

Question #eb26d

Answer 1

28.3

Explanation:

Find the distances between each point. (it's useful to draw a diagram here)
Let's call point (-9,-6) A,(-4,-5) B and (4,-9) C.

Length AB: `x` component is `-9--4=-9+4=5`
`y` component is `-6--5=1`
Now the length of the line is `sqrt(5^2+1^2) = sqrt26` - using pythagoras.

Length BC:
`x` component is 5+4 = 9
`y` component is -5 to -9 = 4
Length = `sqrt(9^2 +4^2) = sqrt97`

Length CA:
`x` component is 4+9 =13
`y` component is -9 to -6 = 3
Length = `sqrt(13^2+3^2)=sqrt(178)`

Now add all the lengths together to find the perimeter:
`sqrt26+sqrt97+sqrt178`

decimal approximation = 28.3 units.