Answer:
1.) 20.2
Step-by-step explanation:
1.) You need to use the distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Find the distance of A to B first:
[tex](-2,2)(3,2)\\\\\sqrt{(3+2)^2+(2-2)^2}\\\\\sqrt{(5)^2+(0)^2}\\\\\sqrt{25} =5[/tex]
B to C:
[tex](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[/tex]
C to A:
[tex](-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[/tex]
Add distances to find the perimeter:
[tex]5+8.1+7.1=20.2[/tex]
2.) Part A:
You need to use the mid-point formula:
[tex]midpoint=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2} )[/tex]
[tex](3,2)(7,11)\\\\(\frac{3+7}{2},\frac{2+11}{2})\\\\(\frac{10}{2},\frac{13}{2})\\\\m=( 5,6.5)[/tex]
Part B:
1. Use the slope-intercept formula:
[tex]y=mx+b[/tex]
M as the slope, b the y-intercept.
Find the slope of the two points A and B using the slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]
Insert slope as m into equation.
Take point A as coordinates [tex](x,y)[/tex] and insert into the equation. Solve for the intercept, b:
[tex](y)=m(x)+b[/tex]
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:
[tex]\frac{1}{2} =-\frac{2}{1}=-2\\[/tex]
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.
