Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle, or a parallelogram. then find the perimeter of the quadrilateral.
a(-3, -2), b(2, -2), c(4, 2), d(-1, 2)
a. parallelogram; (10 + 4ö5) units
b. rectangle; (25 + 2ö5) units
c. square; (5 + 2ö5) units
d. none of these

  a.  parallelogram; (10 + 4√5) units

Step-by-step explanation:

The distance formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

The length AB is ...

  AB = √((2-(-3))² +(-2-(-2))²) = 5

The length BC is ...

  BC = √((4-2)² +(2-(-2))²) = √(4+16) = 2√5

The length of the perimeter of this parallelogram is twice the sum of these:

  P = 2(5+2√5) = 10 +4√5

Lines AB and CD are horizontal, but lines BC and AD are not vertical, so the figure is not a rectangle. It is a parallelogram.

See the explanation.

Step-by-step explanation:

Given  CB║ED And CB≅ED

Since it is given that CB≅ED

The ΔDEF is a reflection of ΔCBE along point 'E'

So, the point 'E' is center of reflection.

And we know under point reflection the images do not change size and shape.

So the sides of both triangles are same, angle will be the same.

Here we can see ∠DEF = ∠BCF  and ∠EDF=∠CBF  also CB=ED

Then ΔDEF≅BCE