Question

Liam is putting up fence around a garden. He has poles located at A(7, 7)
, B(16, 7)
, C(2, 2)
, and 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.

Answer 1

To fence the garden, Liam needs to find the perimeter of the shape formed by the four poles.

To calculate the distance between two points on a coordinate grid, we can use the distance formula, which is given by:

√((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the distance between each pair of adjacent poles:

- Distance between poles A(7, 7) and B(16, 7):
√((16 - 7)^2 + (7 - 7)^2) = √(9^2 + 0^2) = √(81) = 9 feet

- Distance between poles B(16, 7) and D(16, 2):
√((16 - 16)^2 + (7 - 2)^2) = √(0^2 + 5^2) = √(25) = 5 feet

- Distance between poles D(16, 2) and C(2, 2):
√((2 - 16)^2 + (2 - 2)^2) = √((-14)^2 + 0^2) = √(196) = 14 feet

- Distance between poles C(2, 2) and A(7, 7):
√((7 - 2)^2 + (7 - 2)^2) = √(5^2 + 5^2) = √(50) = 7.07 (rounded to the nearest foot) = 7 feet

Now let's add up these distances to find the total perimeter:

9 + 5 + 14 + 7 = 35 feet

Therefore, Liam needs about 35 feet of fencing to fence in the garden.