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)?

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.

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