Coordinate Geometry, Distance Section Mid Point formulas, Condition of Collinearity – Free Math tutorial

Things to Remember: Important Formula for Coordinate Geometry

In this free math tutorial, we understand some of the basic formula list in coordinate geometry. We cover distance formula, collinearity of three points, midpoint and section formula, finding area and centroid of a triangle.

Free Math Education Presentation

Important List of Coordinate Geometry :

Distance formula : If P(x1, y1) and Q(x2, y2) be the end points of any line, then distance ‘d’ between two points is given by

  d = |PQ| = distance formula

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

  d = |PQ| =
 
Section Formula : P(x1, y1) and Q(x2, y2) be the end points of a line and R(x, y) divides the line internally in a ratio m1 and m2, then the coordinates of the point R are given by
  x = ,
y =
Therefore, the formula for the coordinates of a midpoint is given by
  R =
 
Midpoint Formula: If R is the midpoint of a line PQ, then m1 = m2 = m. Then the coordinates of a midpoint R is given by replacing m in place of m1& m2
  R = =
 
Centroid of a Triangle: If the vertices of a triangle are P(x1, y1), Q(x2, y2) and R(x3, y3) respectively, then the coordinates of the centroid of the triangle is given by the formula
  R =
 
Area of a triangle: The area of the triangle formed by the points P(x1, y1), Q(x2, y2) and R(x3, y3), then the area of the triangle is given by
  Area (Triangle PQR) = [x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)]
 
Area of a Quadrilateral: When a quadrilateral is splitting into two parts, both shapes are triangle. Thus area of the quadrilateral can be determined by sum up both the areas of the triangles.
 
  Area (Quadrilateral PQRS) = Area (Triangle PQR) + Area (Triangle QRS)