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2015-05-07T19:47:15+08:00

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Whenever we need to find the distance of two point we are looking for the hypotenuse of a right triangle.

We need to use the Pythagorean Theorem to find the hypotenuse. 

The Pythagorean Theorem is:
a^2+b^2=c^2

This applies to only to right triangles. a and b are the side lengths of the legs while c is the length of the hypotenuse.

In a Cartesian plane the side lengths a and b are represented like this:
(x_a-y_a)=a \\ (x_b-yb)=b

So the Pythagorean Theorem would be:
(x_a-y_a)^2+(x_b-y_b)^2=c^2

We have (x_a,y_a) as (0,2)
and (x_b,y_b) as (-2,0)

We substitute the values to the Pythagorean theorem:
c^2=(0-(-2)^2+(2-0)^2 \\ =2^2+2^2 \\ =4+4 \\ =8

c^2=8 \\ c= \sqrt{8} =2 \sqrt{2}

The distance between the points cannot be negative so only the positive square root is considered. Therefore the distance between the points is 2 \sqrt{2} units.
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