Question 6654
this is a reverse version of the typical question of giving 2 points and finding the distance between them.


It uses Pythagoras' Theorem...


{{{(7-(-5))^2 + (a-(-2))^2 = 13^2}}}
{{{(7+5)^2 + (a+2)^2 = 13^2}}}
{{{(12)^2 + (a+2)^2 = 13^2}}}


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 + (a+2)^2 = 169}}}
{{{(a+2)^2 = 169-144}}}
{{{(a+2)^2 = 25}}}
so, either {{{a+2 = sqrt(25)}}} or {{{a+2 = - sqrt(25)}}}


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.