Question

HELP

Answer 1

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 = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

     =  $\sqrt{(-2-2)^{2}+(-1+4)^{2} }$

    = $\sqrt{25}$

    = 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 =  $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

    =   $\sqrt{(4+2)^{2}+(3-1)^{2} }$

   = √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 =  $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

     =  $\sqrt{(4-0)^{2}+(1-4)^{2} }$

    = √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 = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

    = $\sqrt{(7+5)^{2}+(3-0)^{2} }$

    = √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 =  $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

   =  $\sqrt{(-1+1)^{2}+(-8-6)^{2}}$

   = 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 = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

     = $\sqrt{(-3+7)^{2}+(5-0)^{2}}$

     = 6.4 units units

BC =  6.4 units

CD = 6.4 units

AD = 6.4 units

Perimeter = 25.6 units (F)