SOLUTION: Find the value of a if the points whose coordinates are given are the indicated distance apart. (-2,-5)(a,7);d=13

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Question 6654: Find the value of a if the points whose coordinates are given are the indicated distance apart.
(-2,-5)(a,7);d=13
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
this is a reverse version of the typical question of giving 2 points and finding the distance between them.

It uses Pythagoras' Theorem...

%287-%28-5%29%29%5E2+%2B+%28a-%28-2%29%29%5E2+=+13%5E2
%287%2B5%29%5E2+%2B+%28a%2B2%29%5E2+=+13%5E2
%2812%29%5E2+%2B+%28a%2B2%29%5E2+=+13%5E2

Now, if you know anything about Pythagoras' theorm, you should know about a 5, 12, 13 triangle. We have this here...so a+2=5 --> a=3. But doing it this way is dangerous, because we will miss an answer... see below:

The full proper answer is as follows:

144+%2B+%28a%2B2%29%5E2+=+169
%28a%2B2%29%5E2+=+169-144
%28a%2B2%29%5E2+=+25
so, either a%2B2+=+sqrt%2825%29 or a%2B2+=+-+sqrt%2825%29

ie a+2 = 5 OR a+2 = -5
so a=3 or a=-7

so, a line joining point (-2,-5) to either (3,7) or (-7,7) will give a length of 13.

jon.