# Find Distance Between Two Points

If we are to find the distance between the points $P(0,0)$ and $Q(-2,-3)$, then we can use the Theorem of Pythagoras for this purpose.

$distance (P,Q) = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

therefore, $distance (P,Q) = \sqrt{-5}$ But the answer is undefined. Is this answer and the reason correct?

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You are calculating wrong:

$distance(P,Q) = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}=\sqrt{((-2)^2+(-3)^2)}=\sqrt{(13)}$.

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oh yes! Sorry!! – Samama Fahim Apr 20 '13 at 17:48

You forgot to square. $d(P,Q) = \sqrt{(-2)^2+(-3)^2} = \sqrt{4+9} = \sqrt{13}$.

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It looks like you added the differences $(x_2 - x_1)$ and $(y_2 - y_1)$ without squaring them first!

So you want $$\operatorname {distance}(P, Q)=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13}$$

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