Four points `A(6,3),B(-3,5),C(4,-2)` and `D(x ,2x)` are given in such a way that `((A r e aofD B C))/((A r e aofA B C))=1/2dot`

Four points A(6,3),B(-3,5),C(4,-2) and D(x,3x) are given in such a way that (DBC)/(ABC)=(1)/(2), find x

Four points A(6,3),B(-3,5),C(4,-2) and D(x,3x) are given in such a way that (DBC)/(ABC)=(1)/(2),f in dx

Plot the points A(4,1),B(-3,2),C(2,-3),D(-4,1),E(-4,-4) .

The coordinates of A ,B ,C are (6,3),(-3,5),(4,-2) , respectively, and P is any point (x ,y) . Show that the ratio of the area of P B C to that of A B C is (|x+y-2|)/7dot

A\ (6,3),\ B(-3,5),\ C(4,-2)\ a n d\ D(x ,3x) are four points. If "Delta"D B C :"Delta"A B C=1:2, then x is equal to a. 11/8 b. 8/11 c. 3 d. none of these

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

In triangle A B C ,ifPdotQ ,R divides sidesB C ,A C , and A B , respectively, in the ratio k :1(inor d e r)dot If the ratio ((a r E A P Q R)/(a r e a A B C)) IS 1/3,t h e nk is equal to 1/3 (b) 2 (c) 3 (d) none of these

In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)dot

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot