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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
up vote 4 down vote accepted

Yes, your answers are all correct. Nice work!

(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

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