Section Formula

Section formula in Coordinate Geometry is used to find coordinates when say a point C divides a segment AB in the ratio p:q.

There are two parts of section formula:

Section Formula for Internal division:

A segment that is divided in the ratio m:n, the coordinates of the point C will be calculated using this formula.

C = {[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}

Breaking it down further, the x coordinate is (mx2+nx1)/(m+n) and the y coordinate is (my2+ny1)/(m+n)

Section Formula for External division:

When the point P lies on the external part of the segment, this formula is used to calculate the coordinates.

C = P={[(mx2-nx1)/(m-n)],[(my2-ny1)/(m-n)]}

Breaking it down further, the x coordinate is (mx2-nx1)/(m-n) and the y coordinate is (my2-ny1)/(m-n)

MidPoint Formula:

For a point that lies exactly on the centre of the segment, the midpoint formula is used to find the coordinates.

P={(x1+x2)/2,(y1+y2)/2}

Breaking it down further, the x-coordinate is (x1+x2)/2 and the y-coordinate is (y1+y2)/2

Distance Formula:

This formula is based on the Pythagorean theorem which is used to find the distance between any 2 points.

AB=√[(x2-x1)²+(y2-y1)²]