Answer:
The length is 52 units
Step-by-step explanation:
we know that
The length of the path. is equal to the perimeter of polygon A.B.C.D.E.F
[tex]P=A.B+B.C+C.D+D.E+E.F+A.F[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance A.B
we have
[tex]A(-7,7),B(6,7)[/tex]
substitute in the formula
[tex]d=\sqrt{(7-7)^{2}+(6+7)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(13)^{2}}[/tex]
[tex]d_A_B=13\ units[/tex]
step 2
Find the distance B.C
we have
[tex]B(6,7),C(6,-2)[/tex]
substitute in the formula
[tex]d=\sqrt{(-2-7)^{2}+(6-6)^{2}}[/tex]
[tex]d=\sqrt{(-9)^{2}+(0)^{2}}[/tex]
[tex]d_B_C=9\ units[/tex]
step 3
Find the distance C.D
we have
[tex]C(6,-2),D(3,-2)[/tex]
substitute in the formula
[tex]d=\sqrt{(-2+2)^{2}+(3-6)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-3)^{2}}[/tex]
[tex]d_C_D=3\ units[/tex]
step 4
Find the distance D.E
we have
[tex]D(3,-2),E(3,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6+2)^{2}+(3-3)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]
[tex]d_D_E=4\ units[/tex]
step 5
Find the distance E.F
we have
[tex]E(3,-6),F(-7,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6+6)^{2}+(-7-3)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-10)^{2}}[/tex]
[tex]d_E_F=10\ units[/tex]
step 6
Find the distance A.F
we have
[tex]A(-7,7),F(-7,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6-7)^{2}+(-7+7)^{2}}[/tex]
[tex]d=\sqrt{(-13)^{2}+(0)^{2}}[/tex]
[tex]d_A_F=13\ units[/tex]
step 7
Find the perimeter
[tex]P=A.B+B.C+C.D+D.E+E.F+A.F[/tex]
substitute the values
[tex]P=13+9+3+4+10+13[/tex]
[tex]P=52\ units[/tex]
