What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ?

enter your answer in the box. do not round any side lengths.

what is the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1) ?

enter your answer in the box.

what is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?

enter your answer in the box. do not round any side lengths.

what is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?

15.3 units

20.4 units

30.6 units

52.0 units

(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

The area of the rectangle is .

1. According to the question, the vertices of the rectagle are at , and .

The distance between two vertices on the coordinate plane is

So,

Similarly,

The area of the rectangle is equals to product of length and width of the rectabgle.

So,

Hence, the area of the rectangle is .

Learn more about rectangles here:

link

step-by-step explanation:

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