Basics of Geometry #2: Length, Slope, Midpoint

Length of a Line Segment

The distance between two points on a line segment is called the length of the segment. We usually use the same symbol for the length of the line segment as we do for the segment itself.

So, AB could represent the segment itself, but it could also represent the length of the segment.

We take the absolute value of the difference between two points, ∣b−a∣ or ∣a−b∣.

Example of the distance between two points

Slope

The slope of a line segment is the rate at which the line segment is
increasing or decreasing.

In other words, if we graph the line segment in the xy-plane, the slope will
tell us how fast the segment is going uphill (a positive slope) or
downhill (a negative slope) from left to right. You can find the slope of a
line segment if you have two points that lie on it.

Let’s calculate the slope of this line segment. Suppose we have points with coordinates (x1,y1) and (x2,y2).