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

Answer:

$Cost= \ 47$

Step-by-step 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:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Where

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

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

So, we have:

$d = \sqrt{(4 - (-1))^2 + (2 - 5)^2}$

$d = \sqrt{(4 +1))^2 + -3^2}$

$d = \sqrt{5^2 + -3^2}$

$d = \sqrt{25 + 9}$

$d = \sqrt{34}$

$d = 5.83095189485$

$d = 5.831$ -- Approximated;

If the cost of 1 foot is $8.

5.831 feet will cost:

$Cost= 5.831 * \ 8$

$Cost= \ 46.648$

$Cost= \ 47$ -- Approximated