(1) the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1)
To find area of rectangle we need to find the length and width
Length = distance between (−6, 3) and (−2, −1)
Distance = 
= 
=
=
=
width = Distance between (−6, 3) , (−3, 6)
Distance = 
=
Area = Length * width = 
(2) the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1)
Area of triangle = 
base is the distance between (0,-2) and (8,-2)
Distance =
= 8
To find out height we take two vertices (8,-2) and (9,1)
Height is the change in y values = 1- (-2) = 3
base = 8 and height = 3
So area of triangle = 
(3) the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1)
To find perimeter we add the length of all the sides
Distance between (−2, 1) and (−2, 4) =
= 3
Distance between(−2, 4) and (2, 7) =
= 5
Distance between (2, 7) and (6, 4) =
= 5
Distance between (6, 4) and (6, 1) =
= 3
Distance between (6, 1) and (−2, 1) =
= 8
Perimeter = 3 + 5 + 5 + 3 + 8 = 24
(4) four coordinates are (-7,-1) (-6,4) (3,-3) and (4,2)
Length = Distance between (3,-3) and (4,2) =
= 
Width = Distance between (-6,4) and (4,2) =
= 
Perimeter = 2(lenght + width) = 2*(
+
)
= 30.6 units