Hello dear,

According to the question we are given :

A(-3, 1)

B(0,5)

C(4,8)

D(1,4)

Distance between two points J(X ₁ , Y ₁ ) and K(X ₂ – Y­ ₂ ­) on quadratic plane

= sqrt((X1 – X2) ² + (Y1 – Y2) ² )

Distance AB

= sqrt((-3 - 0) ² + (1 - 5) ² )

= sqrt(9 + 16)

= sqrt(25)

= 5

Distance BC

= sqrt((0 - 4) ² + (5 - 8) ² )

= sqrt(16 + 9)

= sqrt(25)

= 5

Distance CD

= sqrt((4 - 1) ² + (8 - 4) ² )

= sqrt(9 + 16)

= sqrt(25)

= 5

Distance DA

= sqrt((1 – (-3)) ² + (4 - 1) ² )

= sqrt(16 + 9)

= sqrt(25)

= 5

Since, all the sides are equal it clearly specifies that this quadrilateral ABCD is a square.

Thus, Perimeter ABCD    = 4 X length of a side of the square

= 4 X 5

= 20 units