Answer:
the perimeter is 10.99 units.
Step-by-step explanation:
We have a triangle with points in:
X // Y
N 2 // 0
P -1 // -2
M 4 // 0
We can solve for the side of the triangle by subtracting the points to calculate the distance between them, AKA the side of the triangle.
M - N = NM = 4 - 2 = 2 units of X
M - N = NM = 0 - 0 = 0 units of Y
This has a length of 2 units of X and 0 units of Y thus, we already have a line of size 2.
Next side:
N - P = 2 -(-1) = 3 units of x
N - P = 0 - (-2) = 2 units of Y
We have a length of 3 units of X and 2 of Y we use Pythagoras to get the length of NP:
[tex]\sqrt{3^2+2^2} =NP\\\sqrt{9 + 4} = \sqrt{13}[/tex]
Now, we do the same with MP:
M - P = 4 - (-1) = 5 units of X
M - P = 0 - (-2) = 2 units of Y
we solve for MP
[tex]\sqrt{5^2+2^2} = \sqrt{25 + 4} = \sqrt{29}[/tex]
We now add up:
[tex]NM + NP + MP\\2 +\sqrt{13} + \sqrt{29} =\\10.99071608[/tex]
