St. Line

 Line -1 y-intercept (a1) x-intercept (b1) x-coordinate of a point (x1) Find out y-coordinate of the point (y1) slope (m1) w.r.t x-axis angle with x-axis (k1) in degree slope (am1) w.r.t y-axis angle with y-axis (ak1) in degree c1 Equn: a1x + b1y + c1= 0 (a1a)x +(b1a) y +(c1a)=0 Line-2:(case 1) 1st line rotated about y-intercept point by angle ky . Find out y-intercept:  x--coordinate (yintx) & y-co-ordinate (yinty) ------ angle of rotation in degree :(ky) tan of angle(m2) (degree) --tan (k1r ± kyr) (akyr) --(akyra) slope of 2nd line : (anti-clockwise rotation)-(m2a) slope of 2nd line : (clockwise rotation) -(m2b) Equn:    a2ax +b2ay+c2a =0 (anti-clockwise) x +y+=0 a2bx +b2by+c2b =0 (clockwise) x +y+=0 co-ordinate of new point (x2a) & (y2a)=  degree rotation (x2a) ------(y2a) co-ordinate of new point -  Range: to & to degree  (x2b) & (y2b): (x2b) ------(y2b) x-intercept coordinates of line through (x2a,y2a) (ix2a)--(iy2a) x-intercept coordinates of line through (x2b,y2b) (ix2b)--(iy2b) Length of the line segment from (x2a,y2a) to (yintx,yinty) Length of the line segment from (x2b,y2b) to (yintx,yinty) Line-2:(case 2) 1st line rotated about x-intercept point by angle kx . Find out x-intercept x--coordinate & y-co-ordinate ------ angle of rotation in degree :(kx) tan of angle(m2) (degree) --tan (ak1r ± kxr) (akxr) --(akxra) slope of 2nd line : (anti-clockwise rotation)-(m2c) slope of 2nd line : (clockwise rotation) -(m2d) Equn: a2cx +b2cy+c2c =0 x +y+=0 a2dx +b2dy+c2d =0 x +y+=0 co-ordinate of new point (x2c) & (y2c) (x2c) ------(y2c) co-ordinate of new point (x2d) & (y2d) (x2d) ------(y2d) y-intercept coordinates of line through (x2c,y2c) (ix2c)--(iy2c) y-intercept coordinates of line through (x2d,y2d) (ix2d)--(iy2d) Length of the line segment from (x2c,y2c) to (xintx,xinty) Length of the line segment from (x2d,y2d) to (xintx,xinty) Value of (x2, y2) by Matrix method *origin shifted to (a, b) where a is x-coordinate, b is y-coordinate (a)  -- (b) Local co-ordinates of (x1,y1) before rotation (locx1) (locy1) Rotational angle about the new origin (in degree) in + or - Local coordinate of the point in the line after rotation (locx2) (locy2) (x2,y2) the global coordinate of the point in the line after rotation (x2)  ---  (y2) Length * if the origin is shifted to y-interception point, put the value of (yintx, yinty) or x-interception point, put the value of (xintx, xinty) or any value where you want to shift the line parallel keeping the length of the line segment from original origin(0,0) to (x1,y1) intact, and then apply rotation θ about that point in anti-clockwise or clockwise direction and you get the new corresponding co-ordinates (x2, y2)  x2 =[(y1-b)sinθ  +(x1-a)cosθ +a]  y2 =[(y1-b)cosθ  -(x1-a)sinθ +b]