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(C1) Distance Between Two Points

Exam Board: MEI

Question: The points A and B have coordinates (x,1) & (-6,-6). AB = 218\sqrt{218}. Find the possible values of x.

Working out (so far):

(x−−6)2+(1−−6)2=218\sqrt{(x--6)^{2}+(1--6)^{2}}=218

(x−−6)2+49=218(x--6)^{2}+49=218

(x−−6)2=169(x--6)^{2}=169

x−−6=13x--6=13


This is where I'm stuck. This might seem stupid, but it's seriously annoying me. I know that all I need to do is solve the last little bit to get x, but how do I know whether the answers are negative or not? Because the two answers I get are 7 and 19, but which one is negative (if one of them even is negative) and how do I know which one it is?

Thanks in advance. :smile:
Reply 1
Avatar for nerak99
nerak99
13
If you picture the situation, it is clear there will be two points on the line y=1, a particular distance from (-6,-6).

The square root of 169 is plus or minus 13.

Why do you not resolve the --6 to +6?
Reply 2
Avatar for Lucas.
Lucas.
OP
6
Original post by nerak99
If you picture the situation, it is clear there will be two points on the line y=1, a particular distance from (-6,-6).

The square root of 169 is plus or minus 13.

Why do you not resolve the --6 to +6?


Ahhh, that's why I was having trouble working it out. :tongue: I forgot that root 169 was either -13 or +13... :colondollar:

It all makes sense now, thanks. :smile:

Not sure really.. I've never done that. :tongue:

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