Formulas for Coordinate Geometry

Formulas Required  for Solving Coordinate Geometry Questions.

• Distance between two points A(x₁, y₁) and B(x₂, y₂)
  AB = \sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2}

• Slope of line when two points are given (x₁, y₁) and (x₂, y₂)
  m = \frac{(y_{1}- y_{2})}{(x_{1}- x_{2})}

• Slope of line when linear equation is given ax + by = c => – \frac{a}{b}

• Midpoint =\frac{x_{1} +  x_{2}}{2},\frac{y_{1} +  y_{2}}{2}

• 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
  x = \frac{ m x_{2} + nx_{1}}{m + n}

y = \frac{my_{2} + ny_{1} }{m + n}

• 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
  x =\frac{ m x_{2} – nx_{1}}{m – n}

 y = \frac{my_{2} – ny_{1} }{m – n}

• Centroid of a triangle with its vertices (x₁,y₁), (x₂,y₂), (x₃,y₃)
  C = \frac{x_{1}+ x_{2} + x_{3}}{3}, \frac{y_{1}+ y_{2} + y_{3}}{3}

• Area of a Triangle with its vertices A(x₁,y₁), B(x₂,y₂), C(x₃,y₃)
  A =\frac{1}{2} ×[ (x_{1}(y_{2}-y_{3}) + (x_{2}(y_{3}-y_{1})  ) + (x_{3}(y_{1}-y_{2})  )]

• 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
  x= \frac{ m x_{2} + nx_{1}}{m + n} and y= \frac{my_{2} + ny_{1} }{m + n}

• 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).