Answer:
The perimeter of triangle ABC is 15.8 units
Step-by-step explanation:
we know that
The perimeter of a triangle is equal to the sum of its three length sides
[tex]P=AB+BC+AC[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have the coordinates
[tex]A(5,-1),B(-1,1),C(0,-3)[/tex]
step 1
Find the distance AB
we have
[tex]A(5,-1),B(-1,1)[/tex]
substitute in the formula
[tex]d=\sqrt{(1+1)^{2}+(-1-5)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(-6)^{2}}[/tex]
[tex]d_A_B=\sqrt{40}\ units[/tex]
[tex]d_A_B=6.3\ units[/tex]
step 2
Find the distance BC
we have
[tex]B(-1,1),C(0,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3-1)^{2}+(0+1)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(1)^{2}}[/tex]
[tex]d_B_C=\sqrt{17}\ units[/tex]
[tex]d_B_C=4.1\ units[/tex]
step 3
Find the distance AC
we have
[tex]A(5,-1),C(0,-3)[/tex]
substitute in the formula
[tex]d=\sqrt{(-3+1)^{2}+(0-5)^{2}}[/tex]
[tex]d=\sqrt{(-2)^{2}+(-5)^{2}}[/tex]
[tex]d_A_C=\sqrt{29}\ units[/tex]
[tex]d_A_C=5.4\ units[/tex]
step 4
Find the perimeter
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=6.3+4.1+5.4[/tex]
[tex]P=15.8\ units[/tex]
