Answer:
25.6 units
Step-by-step explanation: From the figure we can infer that our triangle has vertices A = (-5, 4), B = (1, 4), and C = (3, -4).
First thing we are doing is find the lengths of AB, BC, and AC using the distance formula:
d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}
where
(x_1,y_1) are the coordinates of the first point
(x_2,y_2) are the coordinates of the second point
- For AB:
d=\sqrt{[1-(-5)]^{2}+(4-4)^2}
d=\sqrt{(1+5)^{2}+(0)^2}
d=\sqrt{(6)^{2}}
d=6
- For BC:
d=\sqrt{(3-1)^{2} +(-4-4)^{2}}
d=\sqrt{(2)^{2} +(-8)^{2}}
d=\sqrt{4+64}
d=\sqrt{68}
d=8.24
- For AC:
d=\sqrt{[3-(-5)]^{2} +(-4-4)^{2}}
d=\sqrt{(3+5)^{2} +(-8)^{2}}
d=\sqrt{(8)^{2} +64}
d=\sqrt{64+64}
d=\sqrt{128}
d=11.31
Next, now that we have our lengths, we can add them to find the perimeter of our triangle:
p=AB+BC+AC
p=6+8.24+11.31
p=25.55
p=25.6
We can conclude that the perimeter of the triangle shown in the figure is 25.6 units.
Read more on Brainly.com - brainly.com/question/12560433#readmore
![\vec{BE}=[-2-(-6);\ 4-10]=[4;\ -6]](https://tex.z-dn.net/?f=%5Cvec%7BBE%7D%3D%5B-2-%28-6%29%3B%5C%204-10%5D%3D%5B4%3B%5C%20-6%5D)
![D(x;\ y)\\\\\vec{ED}=[x-(-2);\ y-4]=[x+2;\ y-4]\\\\\vec{ED}=\vec{BE}\ therefore\\\\ \ [x+2;\ y-4]=[4;\ -6]\to x+2=4\ and\ y-4=-6\\\\x=2\ and\ y=-2\\\\Answer:\ \boxed{A.\ (2;\ -2)}](https://tex.z-dn.net/?f=D%28x%3B%5C%20y%29%5C%5C%5C%5C%5Cvec%7BED%7D%3D%5Bx-%28-2%29%3B%5C%20y-4%5D%3D%5Bx%2B2%3B%5C%20y-4%5D%5C%5C%5C%5C%5Cvec%7BED%7D%3D%5Cvec%7BBE%7D%5C%20therefore%5C%5C%5C%5C%20%5C%20%5Bx%2B2%3B%5C%20y-4%5D%3D%5B4%3B%5C%20-6%5D%5Cto%20x%2B2%3D4%5C%20and%5C%20y-4%3D-6%5C%5C%5C%5Cx%3D2%5C%20and%5C%20y%3D-2%5C%5C%5C%5CAnswer%3A%5C%20%5Cboxed%7BA.%5C%20%282%3B%5C%20-2%29%7D)
