Answer:
[tex]9+\sqrt{41}[/tex]
Step-by-step explanation:
From C-A, it goes from y=1 to y=5, so that 4 units
From A-B, it goes from x = -1 to x = 4, that is 5 units
Now, to find distance from B to C, we need to use the distance formula:
[tex]D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Where the variables are the respective points of B and C,
B (4,5) & C(-1,1)
So x_1 =4, y_1=5, x_2=-1, y_2=1
Plugging into the formula we get:
[tex]D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\D=\sqrt{(1-5)^2+(-1-4)^2}\\D=\sqrt{16+25}\\ D=\sqrt{41}[/tex]
Summing it all (perimeter is sum of 3 sides):
Distance = [tex]4+5+\sqrt{41}\\ =9+\sqrt{41}[/tex]
3rd answer choice is right.
