- If the coordinates of any two points are known, then the distance between the points can easily be found using the distance formula.
- Consider two points and as shown on the graph below.
- The formula to find the distance between the points P and Q is:
- This formula can be derived by using Pythagorean theorem.
- If the coordinates of the endpoints of a line segment are known, then the coordinates of its midpoint can easily be found using the midpoint formula.
- Consider a line segment AB as shown in the figure.
- Let M be the mid-point of AB, then the coordinates of M are given by the formula:
Question 1: Find the distance between the points P and Q shown in the graph.
Solution: It is given that P(1, 2) & Q(4, 6).
Question 2: Find the midpoint of the line segment AB shown in the graph.
Solution: It is given that A(-4, 3) & B(5, 1).
Let be the coordinate of the midpoint of AB.
Hence, the midpoint of segment AB is .
- The distance between the points and is given by:
- The coordinates of the midpoint of a line segment AB where and are given by:
- One must be careful while substituting the values with a negative sign.