Question

Liam is putting up fence around a garden. He has poles located at A(7,7), B(16,7), C(2,2), D(16,2). Each unit on his coordinate grid represents 1 foot. How many feet of fencing does he need to fence in the garden? Round to the nearest Foot. State what strategy you will use to answer the question, explain your choice, and then find the answer.

Answer 1

To find the amount of fencing needed, we will find tge perimeter

To find the perimeter;

Find the distance |AB|, |BC|, |CD| and |DA|

We will use the formula below to find the distances:

`|d|=\sqrt[]{(x_2-x_1)^2+(y_(2-)y_1)^2}`

Distance |AB|

A(7,7), B(16,7)

x₁=7 y₁=7 x₂=16 y₂=7

Substituting into the formula;

`|AB|=\sqrt[]{(16-7)^2+(7-7)^2}`
`=\sqrt[]{9^2+0}`

`=\sqrt[]{9}^2\text{ =9}`

Distance |BC|

B(16,7), C(2,2)

x₁=16 y₁=7 x₂=2 y₂=2

substituting into the formula;

`|BC|=\sqrt[]{(2-16)^2+(2-7)^2}`

`=\sqrt[]{(-14)^2+(5)^2}`
`=\sqrt[]{196+25}`

`=\sqrt[]{221}`
`=14.87`

Distance |CD|

C(2,2), D(16,2)

x₁=2 y₁=2 x₂=16 y₂=2

substituting into the formula;

`|CD|=\sqrt[]{(16-2)^2+(2-2)^2}`

`=\sqrt[]{14^2+0}`
`=\sqrt[]{14^2}=14`

Distance |DA|

D(16,2) A(7,7)

x₁=16 y₁=2 x₂=7 y₂=7

Substituting into the formula;

`|DA|=\sqrt[]{(7-16)^2+(7-2)^2}`

`=\sqrt[]{(-9)^2+(5)^2}`
`=\sqrt[]{81+25}`

`=\sqrt[]{106}=10.30`

Perimeter = |AB|+|BC|+|CD|+|DA|

= 9 + 14.87 + 14 + 10.30

=48.17

≈48

Hence;

48 feet of fencing is needed