Question

Vince uses a coordinate plane to map an amusement park. The ordered pairs are locations of entrances to different rides at the park. He graphs and labels the ordered pairs. Then he connects the points to show the path around the park. What is the length of the path on the grid?

Please Help!

Answer 1

The length is 52 units

Explanation:

we know that

The length of the path. is equal to the perimeter of polygon A.B.C.D.E.F

`P=A.B+B.C+C.D+D.E+E.F+A.F`

The formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

step 1

Find the distance A.B

we have

`A(-7,7),B(6,7)`

substitute in the formula

`d=\sqrt{(7-7)^(2)+(6+7)^(2)}`

`d=\sqrt{(0)^(2)+(13)^(2)}`

`d_A_B=13\ units`

step 2

Find the distance B.C

we have

`B(6,7),C(6,-2)`

substitute in the formula

`d=\sqrt{(-2-7)^(2)+(6-6)^(2)}`

`d=\sqrt{(-9)^(2)+(0)^(2)}`

`d_B_C=9\ units`

step 3

Find the distance C.D

we have

`C(6,-2),D(3,-2)`

substitute in the formula

`d=\sqrt{(-2+2)^(2)+(3-6)^(2)}`

`d=\sqrt{(0)^(2)+(-3)^(2)}`

`d_C_D=3\ units`

step 4

Find the distance D.E

we have

`D(3,-2),E(3,-6)`

substitute in the formula

`d=\sqrt{(-6+2)^(2)+(3-3)^(2)}`

`d=\sqrt{(-4)^(2)+(0)^(2)}`

`d_D_E=4\ units`

step 5

Find the distance E.F

we have

`E(3,-6),F(-7,-6)`

substitute in the formula

`d=\sqrt{(-6+6)^(2)+(-7-3)^(2)}`

`d=\sqrt{(0)^(2)+(-10)^(2)}`

`d_E_F=10\ units`

step 6

Find the distance A.F

we have

`A(-7,7),F(-7,-6)`

substitute in the formula

`d=\sqrt{(-6-7)^(2)+(-7+7)^(2)}`

`d=\sqrt{(-13)^(2)+(0)^(2)}`

`d_A_F=13\ units`

step 7

Find the perimeter

`P=A.B+B.C+C.D+D.E+E.F+A.F`

substitute the values

`P=13+9+3+4+10+13`

`P=52\ units`