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Reviewing Previous Knowledge

A point is represented by its position
units along (OM)
units along (MP)

is the abscissa and is the ordinate of the point .

Distance Formula

Distance between any two points is given by
Distance OP of a point from the origin O(0,0) is

Section Formula

  1. The point P which divides the line joining in the ratio internally is


  1. If P divides the line joining in the ratio externally, then co-ordinates of P are given by

  1. If P is the mid-point of line segment AB, then P is given by


Note: is taken as 1:1 here.


If G is the centroid of a Δ ABC having vertices then the co-ordinates of G are given by


Note: Centroid is the point of intersection of medians of a triangle.

Area of a Triangle

Area of Δ ABC denoted by Δ is given by


1) If the points A, B, C are taken in the anticlockwise sense, the area will be positive, otherwise it will be negative. While doing sums, ignore the negative sign since area cannot be negative.

The above formula can be remembered easily by the notation:


Area of a quadrilateral can be determined by dividing it into two triangles.

Find the area of Δ ABC + area Δ CDA or Area of quadrilateral ABCD using the following notation.

If three points A, B, C are collinear, the area of Δ ABC is zero.
Hence the condition for collinearity of three points is

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