Question 286728
How would we find the distance between a pair of points? 
Our numbers are 
(5, -1) and
(-2,3)
Please please help!!! I am so so so confused!!!



Math can be very confusing.  Try not to worry - this is not too hard.  Here's what you have to know:


Your points are:

(5, -1) and (-2, 3)


Ok, the first set of points are (5, -1) and so the 5 is the "x" and the -1 is the "y".   Since there are TWO sets of points, let's label this FIRST set as:


5 =  {{{x[1]}}}
-1 = {{{y[1]}}}

The second set of points are (-2, 3) and so, the -2 is the "x" and the 3 is the "y".   Now let's label this SECOND set of points this way:


-2 = {{{x[2]}}}
3  = {{{y[2]}}}


Now let's fill in your formula.  The distance formula is:

{{{d = sqrt((x[2]-x[1])^2 + (y[2] -y[1]))^2}}}



We just have to fill in what we know, k?
Remember this info:  


5 =  {{{x[1]}}}
-1 = {{{y[1]}}}


-2 = {{{x[2]}}}
3  = {{{y[2]}}}


Now just fill in the info:


{{{d = sqrt((x[2]-x[1])^2 + (y[2] -y[1]))^2}}}  Distance Formula
{{{d = sqrt((-2 -5)^2 + (3 - (-1)))^2}}}  All the "x" and "y" info is plugged in.   {{{-2 -5 = -7}}} and {{{3 - (-1) = 4}}}
{{{d = sqrt((-7)^2 + (4))^2}}} Now think: {{{(-7)^2 = 49}}} and {{{(4)^2 = 16}}}
{{{d = sqrt (49 + 16)}}}
{{{d = sqrt (65)}}}
{{{d = 8.06225}}} etc  You can round this to:  8.06 


Do you see how you just have to identify your first and second set of ordered pairs.  Then you just plug that info into the formula and solve it.  Not too scary after all, right?


I hope this helps you. :-)