Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and rounded to the nearest tenth.
(please help..)

Part 1) The graph in the attached figure

Part 2) The perimeter is

Part 3) The figure is a square

Part 4) The area is

Step-by-step explanation:

step 1

Plot the quadrilateral

we have

A(10,-5),B(6,-8),C(3,-4),D(7,-1)

using a graphing tool

The quadrilateral in the attached figure

see the attached figure

step 2

Find the perimeter of the figure

The perimeter of the figure  is equal to

the formula to calculate the distance between two points is equal to

Find the length side AB

we have

A(10,-5),B(6,-8)

substitute in the formula

Find the length side BC

we have

B(6,-8),C(3,-4)

substitute in the formula

Find the length side CD

we have

C(3,-4),D(7,-1)

substitute in the formula

Find the length side AD

we have

A(10,-5),D(7,-1)

substitute in the formula

so

The perimeter is equal to

step 3

Determine the slope of the sides

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product is equal to -1)

If two lines are parallel, then their slopes are the same

The formula to calculate the slope between two points is equal to

Find the slope AB

we have

A(10,-5),B(6,-8)

substitute

Find the slope BC

we have

B(6,-8),C(3,-4)

substitute

Find the slope CD

we have

C(3,-4),D(7,-1)

substitute

Find the slope AD

we have

A(10,-5),D(7,-1)

substitute

Compare the slopes

so

Opposite sides are parallel and consecutive sides are perpendicular

The length sides are congruent

therefore

The quadrilateral is a square

step 4

Find the area

The area of a square is

where

b is the length side of the square

we have

the correct option is b

step-by-step explanation:

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation