Answer:
(a) 9.01
(b) 28.42
Step-by-step explanation:
(a)
Step 1. Find the middle of BC:
[tex]M_{BC}=\left(\dfrac{x_B+x_C}2\,,\ \dfrac{y_B+y_C}2\right)=\left(\dfrac{4+1}2\,,\ \dfrac{-1+7}2\right)=\left(\dfrac{5}2\,,\ 3\right)[/tex]
Step 2. Calculate the lenth of AM:
[tex]AM=\sqrt{(x_M-x_A)^2+(y_M-y_A)^2}\\\\AM=\sqrt{(2.5+5)^2+(3+2)^2}= \sqrt{56.25+25}=\sqrt{81.25}\approx9.01[/tex]
(b)
Step 1. Calculate the lenths of sides:
[tex]AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\AB=\sqrt{(4+5)^2+(-1+2)^2}=\sqrt{81+1}= \sqrt{82}\approx9.06\\\\AC=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2} \\\\AC=\sqrt{(1+5)^2+(7+2)^2}=\sqrt{36+81}= \sqrt{117}\approx10.82\\\\ BC=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\\\ BC=\sqrt{(1-4)^2+(7+1)^2}=\sqrt{9+64}= \sqrt{73}\approx8.54[/tex]
Step 2. Add them:
[tex]P=9.06+10.82+8.54=28.42[/tex]
