Answer:
<u><em>1.) 20.2</em></u>
Step-by-step explanation:
1.) You need to use the distance formula:
![d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
Find the distance of A to B first:
![(-2,2)(3,2)\\\\\sqrt{(3+2)^2+(2-2)^2}\\\\\sqrt{(5)^2+(0)^2}\\\\\sqrt{25} =5](https://tex.z-dn.net/?f=%28-2%2C2%29%283%2C2%29%5C%5C%5C%5C%5Csqrt%7B%283%2B2%29%5E2%2B%282-2%29%5E2%7D%5C%5C%5C%5C%5Csqrt%7B%285%29%5E2%2B%280%29%5E2%7D%5C%5C%5C%5C%5Csqrt%7B25%7D%20%3D5)
B to C:
![(3,2)(-1,-5)\\\\\sqrt{(-1-3)^2+(-5-2)^2}\\\\\sqrt{(-4)^2+(-7)^2}\\\\\sqrt{16+49}\\\\\sqrt{65} =8.06=8.1](https://tex.z-dn.net/?f=%283%2C2%29%28-1%2C-5%29%5C%5C%5C%5C%5Csqrt%7B%28-1-3%29%5E2%2B%28-5-2%29%5E2%7D%5C%5C%5C%5C%5Csqrt%7B%28-4%29%5E2%2B%28-7%29%5E2%7D%5C%5C%5C%5C%5Csqrt%7B16%2B49%7D%5C%5C%5C%5C%5Csqrt%7B65%7D%20%3D8.06%3D8.1)
C to A:
![(-1,-5)(-2,2)\\\\\sqrt{(-2+1)^2+(2+5)^2}\\\\\sqrt{(-1)^2+(7)^2}\\\\\sqrt{1+49}\\\\\sqrt{50}=7.07=7.1](https://tex.z-dn.net/?f=%28-1%2C-5%29%28-2%2C2%29%5C%5C%5C%5C%5Csqrt%7B%28-2%2B1%29%5E2%2B%282%2B5%29%5E2%7D%5C%5C%5C%5C%5Csqrt%7B%28-1%29%5E2%2B%287%29%5E2%7D%5C%5C%5C%5C%5Csqrt%7B1%2B49%7D%5C%5C%5C%5C%5Csqrt%7B50%7D%3D7.07%3D7.1)
Add distances to find the perimeter:
![5+8.1+7.1=20.2](https://tex.z-dn.net/?f=5%2B8.1%2B7.1%3D20.2)
2.) Part A:
You need to use the mid-point formula:
![midpoint=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2} )](https://tex.z-dn.net/?f=midpoint%3D%28%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%7D%7B2%7D%20%2C%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%7D%7B2%7D%20%29)
![(3,2)(7,11)\\\\(\frac{3+7}{2},\frac{2+11}{2})\\\\(\frac{10}{2},\frac{13}{2})\\\\m=( 5,6.5)](https://tex.z-dn.net/?f=%283%2C2%29%287%2C11%29%5C%5C%5C%5C%28%5Cfrac%7B3%2B7%7D%7B2%7D%2C%5Cfrac%7B2%2B11%7D%7B2%7D%29%5C%5C%5C%5C%28%5Cfrac%7B10%7D%7B2%7D%2C%5Cfrac%7B13%7D%7B2%7D%29%5C%5C%5C%5Cm%3D%28%20%205%2C6.5%29)
Part B:
1. Use the slope-intercept formula:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
M as the slope, b the y-intercept.
Find the slope of the two points A and B using the slope formula:
![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%20%3D%5Cfrac%7Brise%7D%7Brun%7D)
Insert slope as m into equation.
Take point A as coordinates
and insert into the equation. Solve for the intercept, b:
![(y)=m(x)+b](https://tex.z-dn.net/?f=%28y%29%3Dm%28x%29%2Bb)
Insert the value of b into the equation.
2. Use the mid-point coordinate. Take the slope.
If you need to find the perpendicular bisector, you will take the negative reciprocal of the slope. Switch the sign and flip it. Ex:
![\frac{1}{2} =-\frac{2}{1}=-2\\](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%3D-%5Cfrac%7B2%7D%7B1%7D%3D-2%5C%5C)
Insert the new slope into the slope-intercept equation as m.
Take the mid-point coordinate as (x,y) and insert into the equation with the new points. Solve for b.
Insert the value of b.