Important definitions and formulas - Coordinate Geometry - Class 10 PDF Download

⇒ Distance formula:
Distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by

Distance of any point P(x, y) from the origin O(0, 0) is given by

⇒ Section Formula (Internal division only): 
If point R(x, y) divides the join of P (x₁, y₁) and Q(x₂, y₂) internally in a given ratio (say m₁ : m₂), then the coordinates of the point R are


⇒ Mid-point Formula:
If R is the mid-point, then m₁ = m₂ and the coordinates of R are


❖ If we have to find the ratio in which the join of two points is divided according to given condition, then we take the required ratio as k : 1 and the coordinates of R are

Now, if k is positive, then it is internal division.
⇒ Coordinates of the centroid of a triangle: 
The coordinates of the centroid of a triangle, whose vertices are P(x₁, y₁), Q(x₂, y₂) and  R(x₃, y₃) are
⇒ Area of a Triangle: The area of the triangle formed by the points P(x₁, y₁), Q(x₂, y₂) and R(x₃, y₃) is the numerical value of the expression.


⇒ Area of Quadrilateral: 
Area of a quadrilateral can be found by splitting up the quadrilateral into two triangles and sum up their areas

Thus, Ar (quad. PQRS) = Ar (ΔPQR) + Ar (ΔPRS)