Question

select the correct answer from each drop - down menu.
the approximate length of side xy is
the approximate length of side yz is
the approximate length of side zx is
the approximate perimeter of triangle xyz is

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Find length of $XY$

Let $X(-3,-1)$, $Y(2,-4)$. Then $d_{XY}=\sqrt{(2 + 3)^2+(-4 + 1)^2}=\sqrt{25 + 9}=\sqrt{34}\approx 5.83$.

Step3: Find length of $YZ$

Let $Y(2,-4)$, $Z(-5,-4)$. Then $d_{YZ}=\sqrt{( - 5 - 2)^2+(-4 + 4)^2}=\sqrt{49+0}=7$.

Step4: Find length of $ZX$

Let $Z(-5,-4)$, $X(-3,-1)$. Then $d_{ZX}=\sqrt{(-3 + 5)^2+(-1 + 4)^2}=\sqrt{4 + 9}=\sqrt{13}\approx 3.61$.

Step5: Find perimeter of $\triangle XYZ$

$P=d_{XY}+d_{YZ}+d_{ZX}\approx5.83 + 7+3.61 = 16.44$.

Answer:

The approximate length of side $XY$ is $5.83$ units.
The approximate length of side $YZ$ is $7$ units.
The approximate length of side $ZX$ is $3.61$ units.
The approximate perimeter of triangle $XYZ$ is $16.44$ units.