(i) If a line is at a distance and parallel to -axis, then the equation of the line is .
(ii) If a line is parallel to -axis at a distance from -axis, the the equation of the lines is
The position of points is relative to a given line:
Let and two given points .
(i) The two points are on the same side of the straight line if, and have the same sign.
(ii) The two points are on the opposite sides of the line , if and have opposite sign.
Equation of bisectors of the angle between to intersecting line:
Equation of bisectors and are
Bisectors of the angle containing a given point (h , k) its interior:
Let the equation of two-line and be given by
To obtain the equation of the bisector of the angle containing in its interior, proceed as follows:
(1) First see if and have the same or opposite signs.
(i) If they have the same sign, write
(ii) If they have the opposite sign, write
(2) Write the bisector of the angle containing in its interiro as:
Bisector of the angle, not containing in its interior, is given by ,
Provided and have the same sign.
Pair of Straight Lines:
Consider the equation which is a second degree homogenous equation in and , can be written as which is quadratic in . This gives or which represents a pair of straight lines, with slopes
Change of Axes (Shifting of Origin)
Let the origin is shifted to a point . If are coordinates of a point referred to old axes and are the coordinates of the same points referred to new axes, then
Images of a point with respect to a line:
Let the image of a point with respect to be , then
(i) The image of the point wrto -axis is
(ii) The image wrto -axis is .
(iii) The image of the point wrto mirror is .
(iv) The image of wrto the line mirror is
(v) The image of wrto origin is
(vi) The length of perpendicular from a point to a line is