# Distance between the two points $P$ and $Q$

Let $d(x,y)$ denote the distance between two points, $x$ and $y$, on the plane.

1) $P(2,9),\quad Q(-1,13)\Rightarrow d(P,Q) = 5.$

2) $P(1,-2),\quad Q(2,10)\Rightarrow d(P,Q) = \sqrt{145}.$

3) $P(0,0),\quad Q(-2,-3)\Rightarrow d(P,Q) = \sqrt{13}.$

4) $P(-1,-1),\quad Q(4,4)\Rightarrow d(P,Q) = \sqrt{50}.$

5) $P(6,1),\quad Q(-7,1)\Rightarrow d(P,Q) = 13.$

6) $P(5,10),\quad Q(9,10)\Rightarrow d(P,Q) = 4.$

Are the answers to the above problems correct?

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Yes, they are. Here is the general formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ – gev Apr 20 '13 at 18:41

(In the future, you might want to post what methods you used to determine your answers, so if answers aren't correct, we can point out where/why there's a flaw. For example, I'm assuming you computed distance using the Euclidean distance function:

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

That would have been good to include in your post:

• it makes checking work easier for us,
• if there are errors in answers, we can save you a lot of time by pointing out where may have gone wrong.
• In mathematics, getting the correct answer is usually less important than is using appropriate methods and reasoning.
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nice helpful guidance! +1 – Amzoti Apr 21 '13 at 0:13
@amWhy Thanks, and I'll act upon your advice from the next time. – Samama Fahim Apr 21 '13 at 7:00