The distance between two points on the coordinate geometry is [tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]. The first stripe is 10 inches long.
Given that:
[tex](x_1,y_1) = (2,0)[/tex]
[tex](x_2,y_2) = (5,4)[/tex]
First, we calculate the number of units using distance formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]d = \sqrt{(2 - 5)^2 + (0 - 4)^2}[/tex]
[tex]d = \sqrt{(-3)^2 + (-4)^2}[/tex]
[tex]d = \sqrt{25}[/tex]
Take positive square root
[tex]d = 5[/tex]
From the question, we understand that each unit is 2 inches.
So, the length of the stripe is:
[tex]Length = 2 \times d[/tex]
[tex]Length = 2 \times 5[/tex]
[tex]Length = 10[/tex]
Hence, the first stripe is 10 inches long.
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