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) = (mx2–nx1m−n,my2–ny1m−n)
(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 = √(x2−x1)2+(y2−y1)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!