- Position of a point P in the Cartesian plane with respect to co-ordinate axes is represented by the ordered pair (x, y).
- The line X’OX is called the X-axis and YOY’ is called the Y-axis.
- The part of intersection of the X-axis and Y-axis is called the origin O and the co-ordinates of O are (0, 0).
- The perpendicular distance of a point P from the Y-axis is the ‘x’ co-ordinate and is called the abscissa.
- The perpendicular distance of a point P from the X-axis is the ‘y’ co-ordinate and is called the ordinate.
- Signs of abscissa and ordinate in different quadrants are as given in the diagram:
- Any point on the X-axis is of the form (x, 0).
- Any point on the Y-axis is of the form (0, y).
- The distance between two points P(x1, y1) and Q (x2, y2) is given by
Note. If O is the origin, the distance of a point P(x, y) from the origin O(0, 0) is given by
Section formula. The coordinates of the point which divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m : n are:
The above formula is section formula. The ratio m: n can also be written as : 1 or k : 1, The
co-ordinates of P can also be written as P(x,y) =
The mid-point of the line segment joining the points P(x1, y1) and Q(x2, y2) is
Here m : n = 1 :1.
Area of a Triangle. The area of a triangle formed by points A(x1 y1), B(x2, y2) and C(x3, y3) is given by | ∆ |,
where ∆ =
where ∆ represents the absolute value.
- Three points are collinear if |A| = 0.
- If P is centroid of a triangle then the median divides it in the ratio 2 :1. Co-ordinates of P are given by
Area of a quadrilateral, ABCD = ar(∆ABC) + ar(∆ADC)