The image of `P(a ,b)` on the line `y=-x` is `Q` and the image of `Q` on the line `y=x` is `R` . Then the midpoint of `P R` is (a) `(a+b ,b+a)` (b) `((a+b)/2,(b+2)/2)` (c) `(a-b ,b-a)` (d) `(0,0)`

The image of P(a,b) on the line y=-x is Q and the image of Q on the line y=x is 'R' find the mid-point of 'P' and 'R'

The point Q is the image of the P in line x + y+ 4= 0 and R is the image of Q in line 2x-y + 7=0. If P = (1,6), then the circumcentre of triangle PQR is

The image of the point A (1,2) by the line mirror y=x is the point B and the image of B by the line mirror y=0 is the point (alpha,beta) , then a. alpha=1,beta=-2 b. alpha = 0,beta=0 c. alpha=2,beta=-1 d. none of these

A point P moves such that it is at a constant distance c from the origin. If Q is the image of P in the line mirror y=x and R is the image of Q in the line mirror y= x then locus of R is (a) y^2=x^2 (b) x^2+y^2=2c^2 (c) x y=c^2 (d) x^2+y^2=c^2

If a , b and c are in A P , then the straight line a x+b y+c=0 will always pass through a fixed point whose coordinates are (a) (1,2) (b) (1,-2) (c) (2,3) (d) (0,0)

If (x_1, y_1)&(x_2,y_2) are the ends of a diameter of a circle such that x_1&x_2 are the roots of the equation a x^2+b x+c=0 and y_1&y_2 are the roots of the equation p y^2=q y+c=0. Then the coordinates of the centre of the circle is: (b/(2a), q/(2p)) ( b/(2a), q/(2p)) (b/a , q/p) d. none of these

P (a, b) is the midpoint of a line segment between axes. Show that equation of the line is x/a+y/b=2.

In a three-dimensional coordinate system, P ,Q , and R are images of a point A(a ,b ,c) in the x-y ,y-z and z-x planes, respectively. If G is the centroid of triangle P Q R , then area of triangle AOG is ( O is the origin) (A) 0 (B) a^2+b^2+c^2 (C) 2/3(a^2+b^2+c^2) (D) none of these

The condition on a and b , such that the portion of the line a x+b y-1=0 intercepted between the lines a x+y=0 and x+b y=0 subtends a right angle at the origin, is a=b (b) a+b=0 a=2b (d) 2a=b

The base B C of a A B C is bisected at the point (p ,q) & the equation to the side A B&A C are p x+q y=1 & q x+p y=1 . The equation of the median through A is: (p-2q)x+(q-2p)y+1=0 (p+q)(x+y)-2=0 (2p q-1)(p x+q y-1)=(p^2+q^2-1)(q x+p y-1) none of these