Answer:
The perimeter of triangle ABC is [tex]P=21.8\ units[/tex]
Step-by-step explanation:
The perimeter of triangle ABC is equal to
[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
[tex]A(-4,0),B(-1, 6),C(3,-1)[/tex]
step 1
Find the distance AB
[tex]A(-4,0),B(-1, 6)[/tex]
substitute in the formula
[tex]d_A_B=\sqrt{(6-0)^{2}+(-1+4)^{2}}[/tex]
[tex]d_A_B=\sqrt{(6)^{2}+(3)^{2}}[/tex]
[tex]d_A_B=\sqrt{45}\ units[/tex]
step 2
Find the distance BC
[tex]B(-1, 6),C(3,-1)[/tex]
substitute in the formula
[tex]d_B_C=\sqrt{(-1-6)^{2}+(3+1)^{2}}[/tex]
[tex]d_B_C=\sqrt{(-7)^{2}+(4)^{2}}[/tex]
[tex]d_B_C=\sqrt{65}\ units[/tex]
step 3
Find the distance AC
[tex]A(-4,0),C(3,-1)[/tex]
substitute in the formula
[tex]d_A_C=\sqrt{(-1-0)^{2}+(3+4)^{2}}[/tex]
[tex]d_A_C=\sqrt{(-1)^{2}+(7)^{2}}[/tex]
[tex]d_A_C=\sqrt{50}\ units[/tex]
step 4
Find the perimeter
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=\sqrt{45}+\sqrt{65}+\sqrt{50}=21.8\ units[/tex]
