Coordinate Geometry

Distance Formula: Given the two points (x₁, y₁) and (x₂, y₂), then distance D between these points is given by the formula:

D = sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Section Formula: 

If (x, y) divides (x₁, y₁) and (x₂, y₂) internally in the ratio m n, then,

x = (mx2 + nx1)/(m+n), y = (my2 + ny1)/(m+n).

If (x, y) divides (x₁, y₁) and (x₂, y₂) externally in the ratio m:n, then

 x = (mx2 - nx1)/(m+n), y = (my2 - ny1)/(m+n).

Area of polygon = ½ * [ (x1*y2 – y1*x2) + (x2*y3 _ x3*y3) + …… + (xn*y1 – x1*yn)
where (x1, y1), (x2, y2), ……, (xn, yn) are the vertices of the polygon.

For Straight lines,

More materials:

General formula of figures