Question

Jamie needs to build a fence around his garden , as illustrated by polygon ABCDEF on the coordinate grid below.If each unit represents one yard, what is the total length of Jamie’s fence in yards ?

A.20 yards
B.23 yards
C.26 yards
D.45 yards

Answer 1

C. 26 yards

Explanation:

Total length of Jamie's fence = sum of all distances from one vertex of the polygon to another = AB + BC + CD + DE + EF + FA

Use the distance formula,
`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`, to find the distance between vertexes.

Distance between A(-5, 5) and B(0, 5)

Let,

`A(-5, 5) = (x_1, y_1)`

`B(0, 5) = (x_2, y_2)`

`AB = √((0 -(-5))^2 + (5 - 5)^2)`

`AB = √((5)^2 + (0)^2)`

`AB = √(25 + 0) = √(25)`

`AB = 5`

Distance between B(0, 5) and C(4, 2)

Let,

`B(0, 5) = (x_1, y_1)`

`C(4, 2) = (x_2, y_2)`

`BC = √((4 - 0)^2 + (2 - 5)^2)`

`BC = √((4)^2 + (-3)^2)`

`BC = √(16 + 9) = √(25)`

`BC = 5`

Distance between C(4, 2) and D(1, -2)

Let,

`C(4, 2) = (x_1, y_1)`

`D(1, -2) = (x_2, y_2)`

`CD = √((1 - 4)^2 + (-2 - 2)^2)`

`CD = √((-3)^2 + (-4)^2)`

`CD = √(9 + 16) = √(25)`

`CD = 5`

Distance between D(1, -2) and E(-2, -2)

Let,

`D(1, -2) = (x_1, y_1)`

`E(-2, -2) = (x_2, y_2)`

`DE = √((-2 - 1)^2 + (-2 -(-2))^2)`

`DE = √((-3)^2 + (0)^2)`

`DE = √(9 + 0) = √(9)`

`DE = 3`

Distance between E(-2, -2) and F(-5, 2)

Let,

`E(-2, -2) = (x_1, y_1)`

`F(-5, 2) = (x_2, y_2)`

`EF = √((-5 -(-2))^2 + (2 -(-2))^2)`

`EF = √((-3)^2 + (4)^2)`

`EF = √(9 + 16) = √(25)`

`EF = 5`

Distance between A(-5, 5) and F(-5, 2)

Let,

`A(-5, 5) = (x_1, y_1)`

`F(-5, 2) = (x_2, y_2)`

`FA = √((-5 -(-5))^2 + (2 - 5)^2)`

`FA = √((0)^2 + (-3)^2)`

`FA = √(0 + 9) = √(9)`

`FA = 3`

Total length of Jamie's fence in yards = 5 + 5 + 5 + 5 + 3 + 5 + 3 = 26 yards