Answer :
Answer: 29 goes in the box
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Explanation:
The two endpoints are (-3,1) and (-1,-4)
Apply the distance formula
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-(-1))^2 + (1-(-4))^2}\\\\d = \sqrt{(-3+1)^2 + (1+4)^2}\\\\d = \sqrt{(-2)^2 + (5)^2}\\\\d = \sqrt{4 + 25}\\\\d = \sqrt{29}\\\\d \approx 5.3851648\\\\[/tex]
So the approximate distance is roughly 5.38 units and the exact distance is [tex]\sqrt{29}[/tex] units.
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As a slight alternative, you can plot the point (-3,-4) and draw a right triangle. Then apply the pythagorean theorem to find the length of the hypotenuse. The vertical and horizontal legs are 5 and 2 units respectively.
It turns out that the distance formula is essentially a modified form of the pythagorean theorem.