Question

on the coordinate plane, △mno has vertices m(4, 4), n(5, -7), and o(-6, -6). what is the perimeter of △mno? if necessary, round your answer to the nearest tenth. units

Explanation:

Step1: Calculate the length of MN

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $(x_1,y_1)=(4,4)$ and $(x_2,y_2)=(5, - 7)$.
$MN=\sqrt{(5 - 4)^2+(-7 - 4)^2}=\sqrt{1^2+(-11)^2}=\sqrt{1 + 121}=\sqrt{122}\approx11.0$

Step2: Calculate the length of NO

Use the distance formula with $(x_1,y_1)=(5,-7)$ and $(x_2,y_2)=(-6,-6)$.
$NO=\sqrt{(-6 - 5)^2+(-6+7)^2}=\sqrt{(-11)^2+1^2}=\sqrt{121 + 1}=\sqrt{122}\approx11.0$

Step3: Calculate the length of MO

Use the distance formula with $(x_1,y_1)=(4,4)$ and $(x_2,y_2)=(-6,-6)$.
$MO=\sqrt{(-6 - 4)^2+(-6 - 4)^2}=\sqrt{(-10)^2+(-10)^2}=\sqrt{100+100}=\sqrt{200}=10\sqrt{2}\approx14.1$

Step4: Calculate the perimeter

Perimeter $P=MN + NO+MO\approx11.0+11.0 + 14.1=36.1$

Answer:

$36.1$