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matrenka [14]
2 years ago
6

Find the distance between to points given?

Mathematics
1 answer:
kondor19780726 [428]2 years ago
5 0
<h3>Answer:  29 goes in the box</h3>

===============================================

Explanation:

The two endpoints are (-3,1) and (-1,-4)

Apply the distance formula

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\\\\

So the approximate distance is roughly 5.38 units and the exact distance is \sqrt{29} units.

--------------

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.

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