Notes On Distance Formula - CBSE Class 10 Maths
                  The distance between two points A(x1, y1) and B(x2, y2) is AB =  $\sqrt{{\text{(}{\text{x}}_{\text{2}}\text{-}{\text{x}}_{\text{1}}\text{)}}^{\text{2}}\text{+}{\text{(}{\text{y}}_{\text{2}}\text{-}{\text{y}}_{\text{1}}\text{)}}^{\text{2}}}$   . Distance between any point P(x, y) and origin (0, 0) is    . The coordinates of a point on x - axis is taken as (x, 0) while on y - axis taken as (0, y).   If three points on a graph are given 1) The sum of the distances of two points from a third points is equal to the distance between the first two points, the three points on the graph are collinear. 2) If sum of the squares of any two sides is equal to square of third largest side then three points form a right angle triangle. 3) If all the sides are equal then three points form a equilateral triangle. 4) If any two sides are equal then three points form a isosceles triangle. If four points on a graph are given 1) If opposite sides are equal and the diagonals are also equal then four points form a rectangle. 2) If all sides are equal and the diagonals are also equal then four points form a square. 3) If opposite sides are equal  then four points form a parallelogram. 4) If all sides are equal and the diagonals are not equal then four points form a rhombus. If the A, B and C are three collinear points then AB + BC = AC or AB = AC - BC or BC = AC - AB.

#### Summary

                  The distance between two points A(x1, y1) and B(x2, y2) is AB =  $\sqrt{{\text{(}{\text{x}}_{\text{2}}\text{-}{\text{x}}_{\text{1}}\text{)}}^{\text{2}}\text{+}{\text{(}{\text{y}}_{\text{2}}\text{-}{\text{y}}_{\text{1}}\text{)}}^{\text{2}}}$   . Distance between any point P(x, y) and origin (0, 0) is    . The coordinates of a point on x - axis is taken as (x, 0) while on y - axis taken as (0, y).   If three points on a graph are given 1) The sum of the distances of two points from a third points is equal to the distance between the first two points, the three points on the graph are collinear. 2) If sum of the squares of any two sides is equal to square of third largest side then three points form a right angle triangle. 3) If all the sides are equal then three points form a equilateral triangle. 4) If any two sides are equal then three points form a isosceles triangle. If four points on a graph are given 1) If opposite sides are equal and the diagonals are also equal then four points form a rectangle. 2) If all sides are equal and the diagonals are also equal then four points form a square. 3) If opposite sides are equal  then four points form a parallelogram. 4) If all sides are equal and the diagonals are not equal then four points form a rhombus. If the A, B and C are three collinear points then AB + BC = AC or AB = AC - BC or BC = AC - AB.

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