Question

what is the perimeter of parallelogram wxyz?
√5 + √17 units
2√5 + 2√17 units
16 units
22 units

Explanation:

Step1: Calculate the length of \( WX \)

Use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
For \( W(0,-1) \) and \( X(4,0) \), \( x_1 = 0,y_1=-1,x_2 = 4,y_2 = 0 \).
\( WX=\sqrt{(4 - 0)^2+(0+1)^2}=\sqrt{16 + 1}=\sqrt{17} \)

Step2: Calculate the length of \( WZ \)

For \( W(0,-1) \) and \( Z(-1,-3) \), \( x_1 = 0,y_1=-1,x_2=-1,y_2=-3 \).
\( WZ=\sqrt{(-1 - 0)^2+(-3 + 1)^2}=\sqrt{1+4}=\sqrt{5} \)

Step3: Use the property of parallelogram

In a parallelogram \( WXYZ \), \( WX = YZ=\sqrt{17} \) and \( WZ=XY=\sqrt{5} \).
The perimeter \( P=2(WX + WZ) \)
\( P = 2\sqrt{17}+2\sqrt{5} \)

Answer:

\( 2\sqrt{5}+2\sqrt{17} \) units (the second option)