Question 1144499
<br>
Plot the two points A and B and join them with a line segment.<br>
Then join A and B passing through a point C, where segments AC and BC are vertical and horizontal.<br>
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.<br>
{{{drawing(200,400,-4,6,-4,12,
line(-2,10,4,-2),line(-2,10,-2,-2),line(-2,-2,4,-2),
locate(-2.5,11,"A(-2,10)"),locate(3.5,-2.5,"B(4,-2)"),locate(-2.5,-2.5,"C(-2,-2)")
)}}}<br>
The Pythagorean Theorem now says<br>
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<br>
{{{(10-(-2))^2+(4-(-2))^2 = (AB)^2}}}
{{{12^2+6^2 = (AB)^2}}}
{{{(AB)^2 = 144+36 = 180}}}
{{{AB = sqrt(180) = 6*sqrt(5)}}}<br>
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:<br>
(AB) squared = (difference in x values)^2 + (difference in y values)^2