## Finding the Length of a Line

### Algebra: Lines Help

#### Home | Lines menu | Algebra menu

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:

5^{2} + 13^{2}
= 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.

## Algebra: Line Help

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