In Class IX, you have studied 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).
Let us consider the following situation: A town B is located 36 km east and 15 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. 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(4, 0) and B(6, 0).The points A and B lie on the x-axis.
From the figure you can see that OA = 4units and OB = 6 units.
Let us recall the situation in Section 7.2. Suppose a telephone company wants to position a relay tower at P between A and B is such a way that the distance of the tower from B is twice its distance from A. If P lies on AB, it will divide AB in the ratio 1 : 2 If we take A as the origin O, and 1 km as one unit on both the axis, the coordinates of B will be (36, 15). In order to know the position of the tower, we must know the coordinates of P. How do we find these coordinates?
In your earlier classes, you have studied how to calculate the area of a triangle when
its base and corresponding height (altitude) are given. You have used the formula :
In Class IX, you have also studied Herons formula to find the area of a triangle. Now, if the coordinates of the vertices of a triangle are given, can you find its area? Well, you could find the lengths of the three sides using the distance formula and then use Heron formula. But this could be tedious, particularly if the lengths of the sides are irrational numbers. Let us see if there is an easier way out.
1.The mid-point of the line segment joining the points P
2.The area of the triangle formed by the points3.
3.discusses the Section Formula for the coordinates (x, y) of a point P which divides internally the line segment joining the points.