Question

A farmer is placing fencing material around her triangular garden. The vertices of her garden are located at the points (−1, 5), (4, 2), and (9, −4) on a coordinate grid. If each unit on the grid represents a foot and the material costs $8 per foot, how much will she pay for the material on the side between points (−1, 5) and (4, 2)?

Answer 1

`Cost= \$47`

Explanation:

Given

Vertices: (−1, 5), (4, 2), and (9, −4)

Cost per foot = $8

Required

Determine the cost of fencing (-1, 5) and (4, 2)

First, we need to determine the distance between (-1, 5) and (4, 2)

Distance, d is calculated as follows:

`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Where

`(x_1,y_1) = (-1, 5)`

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

So, we have:

`d = √((4 - (-1))^2 + (2 - 5)^2)`

`d = √((4 +1))^2 + -3^2)`

`d = √(5^2 + -3^2)`

`d = √(25 + 9)`

`d = √(34)`

`d = 5.83095189485`

`d = 5.831` -- Approximated;

If the cost of 1 foot is $8.

5.831 feet will cost:

`Cost= 5.831 * \$8`

`Cost= \$46.648`

`Cost= \$47` -- Approximated