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What is the Section Formula | Distance Formula

Here, you will learn what is the section formula and distance formula and and applications of distance formula.

Let’s begin –

Section Formula – for internal and external division

The co-ordinates of a point dividing a line joining the points P(x1,y1) and Q(x2,y2) in the ratio m : n is given by :

(a)  for internal division : R(x,y) divides line segment PQ, internally.

(x,y) = (mx2+nx1m+n,my2+ny1m+n)

(b) for external division : R(x,y) divides line segment PQ, externally.

(x,y) = (mx2nx1mn,my2ny1mn)

(c) Harmonic Conjugate : If P divides AB internally in the ratio m : n & Q divides AB externally in the ratio m : n then P & Q are said to be harmonic conjugate of each other w.r.t. AB.

Mathematically, 2AB = 1AP + 1AQ i.e. AP, AB & AQ are in H.P.

Distance Formula Between Two Points and its Applications

If A(x1,y1) and B(x2,y2) are two points, then

AB = (x2x1)2+(y2y1)2

Note :

(i)  Three given points A,B and C are collinear, when sum of any two distances out of AB, BC, CA is equal to the remaining third otherwise the points will be the vertices of a triangle.

(ii)  Let A,B,C & D be the four points in a plane. Then the quadrilateral will be :

(a)  Square if AB = BC = CD = DA & AC = BD    AC BD

(b)  Rhombus if AB = BC = CD = DA and AC BD    AC BD

(c)  Parallelogram if AB = BC = CD = DA ; AC BD   AC ⊥̸ BD

(d)  Rectangle if AB = BC = CD = DA ; AC = BD    AC ⊥̸ BD

Hope learnt what is the section formula and distance formula and and applications of distance formula. Tp learn more practice more questions and get ahead in competition. Good Luck!

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