you will learn how to find the distance between the two points whose coordinates are given. You will also study how to find the coordinates of the point which divides a line segment joining two given points in a given ratio. . Distance Formula Let us consider the following situation: A town B is located km east and km north of the town A.
How would you find the distance from town A to town B without actually measuring it. Let us see. This situation can be represented graphically as shown in Fig. .
. You may use the Pythagoras Theorem to calculate this distance. Now, suppose two points lie on the x -axis. Can we find the distance between them?
For instance, consider two points A( , ) and B( , ) in Fig. . . The points A and B lie on the x -axis.
From the figure you can see that OA = units and OB = units. Therefore, the distance of B from A, i.e., AB = OB – OA = – = units. So, if two points lie on the x -axis, we can easily find the distance between them. Now, suppose we take two points lying on the y -axis.
Can you find the distance between them. If the points C( , ) and D( , ) lie on the y -axis, similarly we find that CD = – = units (see Fig. . ).
Next, can you find the distance of A from C (in Fig. . )? Since OA = units and OC = units, the distance of A from C, i.e., AC = = units.
Similarly, you can find the distance of B from D = BD = units. Now, if we consider two points not lying on coordinate axis, can we find the distance between them? Yes! We shall use Pythagoras theorem to do so.
Let us see an example. In Fig. . , the points P( , ) and Q( , ) lie in the first quadrant.
How do we use Pythagoras theorem to find