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}