Important Formulas: Coordinate Geometry | Quantitative for GMAT PDF Download

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Coordinate Geometry

• Coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

Coordinate Geometry Formulas and Basic Concept

• The point of intersection of the x and the y-axis is known as the origin. At this point, both x and y are 0.
• The values on the right-hand side of the x-axis are positive and the values on the left-hand side of the x-axis are negative.
• Similarly, on the y-axis, the values located above the origin are positive and the values located below the origin are negative.

Formulas for Coordinate Geometry Questions

• Distance between two points A(x₁, y₁) and B(x₂, y₂)
• Slope of line when two points are given (x₁, y₁) and (x₂, y₂)
• Slope of line when linear equation is given
• 
• The co-ordinates of a point R(x,y) that divides a line segment joining two points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m:n is given by
  
• The co-ordinates of a point R(x,y) that divides a line segment joining two points A(x₁, y₁) and B(x₂, y₂) externally in the ratio m:n is given by
  
• Centroid of a triangle with its vertices (x₁, y₁), (x₂, y₂), (x₃,y₃)
  
• Area of a Triangle with its vertices A(x₁, y₁), B(x₂, y₂), C(x₃,y₃)
  
• Division of a line segment by a point

  If a point p(x, y) divides the join of A(x₁, y₁) and B(x₂, y₂), in the ratio m: n, then
  

• The equation of a line in slope intercept form is Y= mx+ c, where m is its slope.

  The equation of a line which has gradient m and which passes through the point (x₁, y₁) is =

  y – y₁ = m(x – x₁).

Example: If the slope of a line is -2/3 and it passes through the point (2, 5), find the equation of the line in point-slope form.
Answer: Equation of the line passing through points P(3, 8) and Q(5, -2):


Using the point-slope form: y – y1 = m(x – x1)
y – 8 = -5(x – 3)
y – 8 = -5x + 15
y = -5x + 23