## Finding the Length of a Line

### Algebra: Lines Help

The easiest way to show you how to do this is by working out an example.

Example: Find the distance between (-2,8) and (-7,-5).

This is not rocket science.

Step 1: Find the distance between the x-coordinates. We do that by subtracting one number from the other and then finding its absolute value.
We have |-2 - (-7)| = |5| = 5

Step 2: Do the same thing with the y-coordinates.
|8 - (-5)| = |13| = 13

The geniuses among you will have noticed that it doesn't matter which way you subtract the numbers because the absolute value of the answer would be the same anyway.

Step 3: Square both your answers, add them, and take the square root. Doing that we get:
52 + 132 = 25 + 169 = 194
Taking the square root of 194 and rounding to 2 decimals places we get the distance = 13.93

By the way, what you are actually doing is using the Pythagorean theorem on an imaginary right-angle triangle with the line joining the two lines being the hypotenuse. Try it some time - get some Cartesian graph paper, put your 2 points on the graph, make a right angle triangle out of it and you'll see what I mean. 