Distance Formula, Section Formula

Things to remember

→ The formula remains the same if the points P (x₁,y₁) and Q (x₂,y₂) are taken in different quadrants.

→ If a point lies on x-axis, its ordinate is zero. Therefore, any point on x-axis can be taken as (x,0).

→ If a point lies on y-axis, its abscissa is zero. Therefore, any point on y-axis can be taken as (0,y).

→ To prove that a quadrilateral is a

  1) rhombus, show that all sides are equal.

  2) square, show that all sides are equal and diagonals are equal.

  3) parallelogram, show that opposite sides are equal.

  4) rectangle, show that opposite sides are equal and diagonals are equal.

→ To prove that a triangle is a

 1) scalene, show that none of the sides are equal.  

2) isosceles, show that two sides are equal.

3) equilateral, show that all sides are equal.

 4) right-angled triangle, show that square on one side equals