We can find the distance between two points using an expression derived from the Pythagorean Theorem. Suppose we have two points and and we want to find the distance between them. Remember the Pythagorean Theorem for finding the length of the hypotenuse, c, of right triangle with sides, a and b, is
For example, take the points (-2,1) and (5,4) again. We can see their location and the slope of the line connecting them.
Now we have a and b of the pythagorean theorem and all we
need to do is some arithmetic. Remember our equation:
The final topic for lines is the relationship between two lines on the same axes. Two lines are parallel if the have the same slope, and two lines are perpendicular if .