Introduction
In this chapter, 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.
Take a look at the canvas below. It's just an empty page. It does not have any details. It will be very hard to give directions to someone to draw something on this precisely. For example, what directions can you give someone to make them draw the face of a cat. Maybe we can say something like start at the left corner, draw a line towards east etc etc.
Did you draw the line
Since a simple empty paper has no information, we cannot do much with it. What can we add to this paper to make it more useful?
A simple insight that people found is that, if you draw horizontal and vertical lines on this paper we can create an abstraction which represents a lot of things.
We have also studied earlier that to locate the position of a point on a plane, we require a pair of coordinate axes. The distance of a point from the y-axis is called its x-coordinate, or abscissa. The distance of a point from the x-axis is called its y-coordinate, or ordinate.
The coordinates of a point on the x-axis are of the form (x, 0), and of a point on the y-axis are of the form (0, y).
Here is a play for you. Draw a set of a pair of perpendicular axes on a graph paper. Now plot the following points and join them as directed: Join the point A(4, 8) to B(3, 9) to C(3, 8) to D(1, 6) to E(1, 5) to F(3, 3) to G(6, 3) to H(8, 5) to I(8, 6) to J(6, 8) to K(6, 9) to L(5, 8) to A. Then join the points P(3.5, 7), Q (3, 6) and R(4, 6) to form a triangle. Also join the points X(5.5, 7), Y(5, 6) and Z(6, 6) to form a triangle. Now join S(4, 5), T(4.5, 4) and U(5, 5) to form a triangle. Lastly join S to the points (0, 5) and (0, 6) and join U to the points (9, 5) and (9, 6). What picture have you got?
Also, we have seen that a linear equation in two variables of the form ax + by + c = 0, (a, b are not simultaneously zero), when represented graphically, gives a straight line.
Further, we have also seen that the graph of