Straight Lines

Let the lines 3x-4y- =0, 8x-11y-33=0, and 2x-3y+ =0 be concurrent. If the image of the point (1,2) in the line 2x-3y+ =0 is ( 5713, -4013 ), then | | is equal to

1. 91
2. 113
3. 101
4. 84

Let the points ( 112, ) lie on or inside the triangle with sides x+y=11, x+2y=16 and 2x+3y=29. Then the product of the smallest and the largest values of is equal to :

1. 22
2. 33
3. 55
4. 44

Let the area of a PQR with vertices P(5,4), Q(-2,4) and R(a,b) be 35 square units. If its orthocenter and centroid are O (2, 145 ) and C(c,d) respectively, then c+2d is equal to

1. 3
2. 73
3. 2
4. 83

A rod of length eight units moves such that its ends A and B always lie on the lines x-y+2=0 and y+2=0, respectively. If the locus of the point P, that divides the rod AB internally in the ratio 2:1 is 9 (x2+ y2+ xy+ x+28y )-76=0, then - - is equal to :

1. 24
2. 22
3. 21
4. 23

Let the triangle PQR be the image of the triangle with vertices (1,3),(3,1) and (2,4) in the line x+2y=2. If the centroid of is the point ( , ), then 15( - ) is equal to :

1. 21
2. 19
3. 22
4. 24

Let A(6,8), B(10 ,-10 ) and C(-10 ,10 ), be the vertices of a triangle. If L(a,9) and G(h,k) be its orthocenter and centroid respectively, then (5a-3h+6k+100 2 ) is equal to .

Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then (QR)2 is equal to .

A variable line L passes through the point (3, 5) and intersects the positive coordinate axes at the points A and B. The minimum area of the triangle OAB, where O is the origin, is :

1. 35
2. 25
3. 30
4. 40

A ray of light coming from the point P(1, 2) gets reflected from the point Q on the x-axis and then passes through the point R(4, 3). If the point S(h, k) is such that PQRS is a parallelogram, then hk2 is equal to:

1. 60
2. 70
3. 80
4. 90

Two vertices of a triangle ABC are A(3, -1) and B(-2, 3), and its orthocentre is P(1, 1). If the coordinates of the point C are ( , ) and the centre of the circle circumscribing the triangle PAB is (h, k), then the value of ( + ) + 2(h + k) equals

1. 81
2. 15
3. 51
4. 5