Section Formula

If point P lies on

If point P lies on the line segment AB such that PA:PB = m:n, then P divides AB internally in the ratio m:n.

If A(x1

If A(x1,y1) and B(x2,y2) are given points and P divides AB internally in the ratio m:n, then P is given by x=(mx2+nx1)/(m+n), y=(my2+ny1)/(m+n).

Perpendiculars are drawn to the x

Perpendiculars are drawn to the x-axis, and similar triangles AQP and PRB are used. From similarity, m/n=(x-x1)/(x2-x)=(y-y1)/(y2-y). After cross mult

The midpoint of AB has coordinates

The midpoint of AB has coordinates ((x1+x2)/2,(y1+y2)/2). It is obtained by putting m=n in the section formula.

The centroid is the point

The centroid is the point of intersection of the medians of a triangle. If A(x1,y1), B(x2,y2), and C(x3,y3) are the vertices, then the centroid is giv