SOLUTION: If A(-2,10) and B(4,-2) then AB=?

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Question 1144499: If A(-2,10) and B(4,-2) then AB=?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Plot the two points A and B and join them with a line segment.

Then join A and B passing through a point C, where segments AC and BC are vertical and horizontal.

Triangle ACB will be a right triangle; the length of AB can be found using the Pythagorean Theorem. The lengths of the legs are easy to find, because segments AC and BC are vertical and horizontal.



The Pythagorean Theorem now says

square of length of AC (difference in y values of A and B), plus square of length of BC (difference in x values of A and B) equals square of length of AB

%2810-%28-2%29%29%5E2%2B%284-%28-2%29%29%5E2+=+%28AB%29%5E2
12%5E2%2B6%5E2+=+%28AB%29%5E2
%28AB%29%5E2+=+144%2B36+=+180
AB+=+sqrt%28180%29+=+6%2Asqrt%285%29

Draw a picture like this (at least in your mind) when you solve the next few problems like this; after that you should be able to see the calculation that is required without drawing the picture:

(AB) squared = (difference in x values)^2 + (difference in y values)^2