Question

9
select the correct answer from each drop - down menu.
find the approximate side lengths and perimeter of quadrilateral wxyz. if necessary, round your answers to the nearest hundredth.
the approximate length of segment wx is units.
the approximate length of segment xy is units.
the approximate length of segment yz is units
the approximate perimeter of quadrilateral wxyz is units.
reset next

Explanation:

Step1: Determine the coordinates

From the graph, \(W(3,1)\), \(X(6, - 1)\), \(Y(7,-3)\), \(Z(3,-3)\)

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

• For \(WX\):

\(x_1 = 3,y_1 = 1,x_2=6,y_2=-1\)
\(d_{WX}=\sqrt{(6 - 3)^2+(-1 - 1)^2}=\sqrt{9 + 4}=\sqrt{13}\approx3.61\)

• For \(XY\):

\(x_1 = 6,y_1=-1,x_2 = 7,y_2=-3\)
\(d_{XY}=\sqrt{(7 - 6)^2+(-3+1)^2}=\sqrt{1+4}=\sqrt{5}\approx2.24\)

• For \(YZ\):

\(x_1 = 7,y_1=-3,x_2 = 3,y_2=-3\)
\(d_{YZ}=\sqrt{(3 - 7)^2+(-3 + 3)^2}=\sqrt{16+0}=4\)

• For \(ZW\):

\(x_1 = 3,y_1=-3,x_2 = 3,y_2=1\)
\(d_{ZW}=\sqrt{(3 - 3)^2+(1 + 3)^2}=\sqrt{0 + 16}=4\)

Step3: Calculate the perimeter \(P\)

\(P=d_{WX}+d_{XY}+d_{YZ}+d_{ZW}\)
\(P\approx3.61+2.24 + 4+4=13.85\)

Answer:

The approximate length of segment \(WX\) is \(3.61\) units.
The approximate length of segment \(XY\) is \(2.24\) units.
The approximate length of segment \(YZ\) is \(4\) units.
The approximate perimeter of quadrilateral \(WXYZ\) is \(13.85\) units.