Answer:
We find the perimeter using the distance formula between two points.
1) A(2, -4), B(-2, -1), C(-5, -5), D(-1, -8)
AB = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
= [tex]\sqrt{(-2-2)^{2}+(-1+4)^{2} }[/tex]
= [tex]\sqrt{25}[/tex]
= 5 units
Similarly, BC = 5 units
CD = 5 units
AD = 5 units
Perimeter = AB+BC+CD+AD = 20 units (E)
2) X(-2, 1), Y(4, 3), Z(5, -1)
XY = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
= [tex]\sqrt{(4+2)^{2}+(3-1)^{2} }[/tex]
= √40 = 6.3
Similarly, YZ = √17 = 4.1
XZ = 7.3
Perimeter = XY+YZ+XZ = 17.7 units (C)
3) A(0, 4), B(4, 1), C(4, -4), D(-4, -4), E(-4, 1)
AB = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
= [tex]\sqrt{(4-0)^{2}+(1-4)^{2} }[/tex]
= √25 = 5 units
BC = 5 units
CD = 8 units
DE = 5 units
AE = 5 UNITS
Perimeter = 28 units (B)
4) . T(-5, 0), U(7, 3), V(9, -6), W(-3, -9)
TU = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
= [tex]\sqrt{(7+5)^{2}+(3-0)^{2} }[/tex]
= √153 = 12.4 units
UV = 9.2 units
VW = 12.4 units
TW = 9.2 units
Perimeter = 43.2 units (D)
5) S(-1, 6), T(-1, -8), U(7, -8)
ST = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
= [tex]\sqrt{(-1+1)^{2}+(-8-6)^{2}}[/tex]
= 14 units
TU = 8 units
SU = 16.1 units
Perimeter = 38.1 units (A)
6) A(-7, 0), B(-3, 5), C(2, 1), D(-2, -4)
AB = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
= [tex]\sqrt{(-3+7)^{2}+(5-0)^{2}}[/tex]
= 6.4 units units
BC = 6.4 units
CD = 6.4 units
AD = 6.4 units
Perimeter = 25.6 units (F)
