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

Are the points (3,4) and (2,-6) on the same or opposite sides of the line 3x-4y=8?

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

Statement I The points (3,2) and (1,4) lie on opposite side of the line 3x-2y-1 =0 Statement II The algebraic perpendicular distance from the given the point to the line have opposite sign

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.

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.

If P is a point (x,y) on the line y=-3x such that P and the point (3,4) are on the opposite sides of the line 3x-4y-8=0, then :

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

Equation of line passing through the point (2,3,1) and parallel to the line of intersection of the planes: x-2y-z+5=0 and x+y+3z=6 is:

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.