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(\(x_1,y_1\)) and Q(\(x_2,y_2\)) in the ratio m : n is given by :
(a) for internal division : R(x,y) divides line segment PQ, internally.
(x,y) = (\(mx_2 + nx_1\over {m+n}\),\(my_2 + ny_1\over {m+n}\))
(b) for external division : R(x,y) divides line segment PQ, externally.
(x,y) = (\(mx_2 – nx_1\over {m-n}\),\(my_2 – ny_1\over {m-n}\))
(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, \(2\over AB\) = \(1\over AP\) + \(1\over AQ\) i.e. AP, AB & AQ are in H.P.
Distance Formula Between Two Points and its Applications
If A(\(x_1,y_1\)) and B(\(x_2,y_2\)) are two points, then
AB = \(\sqrt{{(x_2-x_1)}^2 + {(y_2-y_1)}^2}\)
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 \(\perp\) BD
(b) Rhombus if AB = BC = CD = DA and AC \(\ne\) BD AC \(\perp\) BD
(c) Parallelogram if AB = BC = CD = DA ; AC \(\ne\) BD AC \(\not\perp\) BD
(d) Rectangle if AB = BC = CD = DA ; AC = BD AC \(\not\perp\) 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!
