mei is knitting a scarf with diagonal stripes before she began she laid out the pattern on a coordinate grid where each unit represented 2 inches. On the grid the first stripe began at (2,0) and ended at (5,4). All the stripes are the same length. How many inches long is each stripe on the scarf?

Question

25-08-2021
Mathematics

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mei is knitting a scarf with diagonal stripes before she began she laid out the pattern on a coordinate grid where each unit represented 2 inches. On the grid the first stripe began at (2,0) and ended at (5,4). All the stripes are the same length. How many inches long is each stripe on the scarf?

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MrRoyal MrRoyal · Answer 1 · 2021-08-27T22:19:42+02:00

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.