Show that (1,2) and (-3,-2) lie on the same side of 2x - 3y + 5 = 0.

If the point (1,2) and (34) were to be on the same side of the line 3x-5y+a=0 then

Find the interval of alpha for which (alpha, alpha^2, alpha) and (3, 2, 1) lies on same side of x+y-4z+2=0 .

Are the points (2,1) and (-3,5) on the same or opposite side of the line 3x - 2y + 1 = 0 ?

The equation of the line AB is y = x . If A and B lie on the same side of the line mirror 2x-y = 1 , then the equation of the image of AB is

Find the ratio in which the plane ax+by+cz+d=0 divides the join of the points P(x_1,y_1,z_1) and Q(x_2,y_2,z_2) lying on the plane. Hence, show that the points P(1,-2,3) and Q(0,0,-1) lie on opposite sides of the plane 2x+5y+7z=3.

Statement 1 :If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2 : The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.

If A((sin alpha)/3 - 1,(cos alpha)/2 - 1) and B(1,1) alpha in [ -pi,pi] are two points on the same side of the line 3x - 2y +1 = 0 then alpha belongs to the interval

A rectangle has opposite vertices at the points (1,2) and (5, 5). If the other vertices lie on the line x=3, find the equation of the sides of the rectangle.

Show that the four points of intersection of the lines : (2x-y + 1) (x-2y+3) = 0 , with the axes lie on a circle and find its centre.

Show that the three straight lines 2x-3y + 5 = 0 , 3x + 4y - 7 = 0 and 9x- 5y + 8 = 0 meet in a point