The perimeter of the quadrilateral ABCD formed by A(-3,1),B(0,5),C(4,8),D(1,4) taken in that order is
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
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