Problem 1
Answer: 6.7
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Work Shown:
The two points are [tex](x_1,y_1) = (1,-2)[/tex] and [tex](x_2,y_2) = (4,4)[/tex]
Apply the distance formula to get the following
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (-2-4)^2}\\\\d = \sqrt{(-3)^2 + (-6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d \approx 6.7082039\\\\d \approx 6.7\\\\[/tex]
The distance between the two endpoints is roughly 6.7 units. This is the same as saying the segment is roughly 6.7 units long.
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Problem 2
Answer: 3.6
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Work Shown:
We'll use the distance formula here as well.
This time we have the two points [tex](x_1,y_1) = (3,1)[/tex] and [tex](x_2,y_2) = (5,-2)[/tex]
The distance between them is...
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-5)^2 + (1-(-2))^2}\\\\d = \sqrt{(3-5)^2 + (1+2)^2}\\\\d = \sqrt{(-2)^2 + (3)^2}\\\\d = \sqrt{4 + 9}\\\\d = \sqrt{13}\\\\d \approx 3.6055513\\\\d \approx 3.6\\\\[/tex]
This distance is approximate.
