Suppose a cartesian line L is given by the equation xa yb

Suppose a cartesian line L is given by the equation x/a + y/b = 1, where a and b are non-zero real numbers. Let R_pi be the counterclockwise rotation of the plane by 180 degrees with the center at (0,0). Find an equation of R_pi (L) in the form x/u + y/v = 1. Suppose a cartesian line L is given by the equation a middot x + b middot y + c = 0, where a, b, and c are three real numbers such that a^2 + b^2 > 0. Let R_pi be the counterclockwise rotation of the plane by 180 degrees with the center at (0,0). Find an equation of R_pi (L) in the form u middot x + v middot y + w = 0.

Solution

1.when the xy plane is rotated counterwise by 180 degrees then in in the new plane the x axis will remain the same but the y axis will be inverted. Thus if (u, v) be the intercepts in New plane then u=a and v=-b.any straight line in New plane will be mirror image about x axis of the original straight line. Thus eequation of straight line in New plane will be x/a-y/b=1

2. From part 1,we can say that equation of striated line ax+by+c=0 in New plane will be ax-by+c=0.