Given:
The vertices of the garden on a coordinate grid are (−1,5), (4,2) and (9,−4).
Each unit on the grid represents a foot and the material costs $8 per foot.
To find:
The cost for the material on the side between points (−1,5) and (4,2).
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the above formula, the distance between points (−1,5) and (4,2) is
[tex]d=\sqrt{(4-(-1))^2+(2-5)^2}[/tex]
[tex]d=\sqrt{(4+1)^2+(-3)^2}[/tex]
[tex]d=\sqrt{(5)^2+(-3)^2}[/tex]
On further simplification, we get
[tex]d=\sqrt{25+9}[/tex]
[tex]d=\sqrt{34}[/tex]
[tex]d\approx 5.83[/tex]
Now,
1 unit = 1 foot and 1 foot material costs is $8.
So, 1 unit material cost is $8.
Cost of material for 5.83 units is
[tex]5.83\times 8=46.64[/tex]
Therefore, the cost for the material on the side between points (−1,5) and (4,2) is $46.64.
