So far we’ve looked at examples involving the midpoint of a line segment. In this lesson, we will learn how to find the **length of any line segment** using the distance formula â€“ a formula derived from the *Pythagorean theorem â€“ *and how we can use it to compare distances in a map.

- If you’d like to touch up on the
*Pythagorean theorem*, feel free to review this video. Feel free to skip it if you’re comfortable with it.

Now, let’s take a look at two examples where we find the distance between two coordinates.

#### Use the distance formula to solve problem

Question 1:To make round parts, programmable machine tools often use a coordinate system with the origin at the center of the part. How far apart are the centers of the mounting holes A and B in this cam? The coordinates are in centimeters. Round your answer to the nearest tenth.

Question 2:An air ambulance service uses a grid system to help estimate flying times and fuel requirements. Coordinates on this grid are distances in kilometers east and north of a reference point on the lower left corner of a map of northern Ontario. A helicopter ambulance picks up a patient at point P(96, 197). The nearest hospitals that can provide the treatment the patient needs are in Timmins at T(200, 296) and Sudbury at S(232, 80).

To which hospital should the helicopter take the patient?

Finally, let’s apply our knowledge to finding the **length of a median** in a triangle. Not only does this relate to what we just learned above, we had a similar problem in our previous lesson when we found an equation that represented the median. Notice here we’re finding the length, so it’s a little less work.