`G` is the centroid of triangle `A B Ca n dA_1a n dB_1` are rthe midpoints of sides `A Ba n dA C ,` respectively. If `"Delta"_1` is the area of quadrilateral `G A_1A B_1a n d"Delta"` is the area of triangle `A B C ,` then `"Delta"//"Delta"_1` is equal to a.`3/2` b. `3` c. `1/3` d. none of these

G is the centroid of triangle ABC and A_(1) and B_(1) are the midpoints of sides AB and AC , respectively.If Delta_(1) is the area of quadrilateral GA_(1)AB_(1) and Delta is the area of triangle ABC, then (Delta)/(Delta_(1)) is equal to

Find the area of triangle ABC , the midpoints of whose sides AB, BC and CA are D(3,-1), E(5, 3) and F(1,-3) respectively.

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a)2 (b) 2/3 (c) 1/3 (d) 3

Let the area of a given triangle ABC be Delta. Points A_1, B_1, and C_1 , are the mid points of the sides BC,CA and AB respectively. Point A_2 is the mid point of CA_1. Lines C_1A_1 and A A_2 meet the median BB_2 points E and D respectively. If Delta_1 be the area of the quadrilateral A_1A_2DE, using vectors or otherwise find the value of Delta_1/Delta

The vertices of a Delta ABC are A (2, 3, 1), B (-2, 2, 0) and C(0, 1, -1) . What is the area of the triangle?

If the area of a square with side a is equal to the area of a triangle with base a, then the altitude of the triangle is (a)/(2) (b) a (c) 2a (d) 4a

If Delta_1=|(1,0),(a,b)| and Delta_2=|(1,0),(c,d)| , then Delta_2Delta_1 is equal to :

If A(-3,4),B(1,-2),C(5,6) and D(x,-4) are the vertices of a quadrilateral such that area of Delta ABC=Delta ACD then x=