1)D is mid point of side ac and G divides BD in ratio 2:1. the coordinates of G are:

2) if O is origin, then the area of triangleAOB is:

3) The segments joining A(3,2) and B(7,3) is extended along a straight line till C such that AC is 4 times AB> the coordinates of C are:

4) find distance between the poiints

(a cos20 + b sin20,0) and (0, a sin20 + b cos20)

5) ABCD is a parallelogram whose diagonals are intersecting at P(6,4). find coordinates of A and D.

6) find the coordinates of the points of trisection of segmentAB where A(-3,2) and B(9,5).

7) the two opposite vertices of a square are (-1,2) and (3,2). find the coordinates of the other two vertices.

8) find ratio in which the line 3x+4y-9=0 divides the line segment joining points (1,3) and (2,7).

9) find centroid of triangleABC whose sides are given by 2x+3y=12; x-y=1,y=0.

4. Let

6.

Let A (–3, 2) and B (9, 5) be the given points. Let the points of trisection be C and D. Then, AC = CD = BD

CB = CD + DB = 2λ and

AC = AC + CD = 2λ

⇒ AC : CB = λ: 2λ = λ : 2 and

AD : DB = 2λ : λ = 2:1

So, C divides AB internally in the ratio 1:2, while D divides internally in the ratio 2:1. Thus, the coordinates of C and D are

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