




Line 1 



yintercept (a1) 



xintercept (b1) 



xcoordinate of a point (x1) 



Find out 



ycoordinate of the point (y1) 



slope (m1) w.r.t xaxis 



angle with xaxis (k1) in degree 



slope (am1) w.r.t yaxis 



angle with yaxis (ak1) in degree 



c1 



Equn: a1x + b1y + c1= 0 
(a1a)x
+(b1a)
y +(c1a)=0 


Line2:(case 1) 1st line
rotated about yintercept point by angle ky . Find out 



yintercept: xcoordinate (yintx) & ycoordinate
(yinty) 
 


angle of rotation in degree :(ky) 



tan of angle(m2)
(degree) tan
(k1r ± kyr) 
(akyr)
(akyra) 


slope of 2nd line : (anticlockwise rotation)(m2a) 



slope of 2nd line : (clockwise rotation) (m2b) 



Equn: a2ax +b2ay+c2a =0
(anticlockwise) 
x
+y+=0 


a2bx +b2by+c2b =0
(clockwise) 
x
+y+=0 


coordinate of new point (x2a) & (y2a)=
degree rotation 
(x2a)
(y2a) 


coordinate of new point 
Range:
to
&
to
degree
(x2b) & (y2b): 
(x2b)
(y2b) 


xintercept coordinates of line through (x2a,y2a) 
(ix2a)(iy2a) 


xintercept 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) 







Line2:(case 2) 1st line
rotated about xintercept point by angle kx . Find out 



xintercept xcoordinate & ycoordinate 
 


angle of rotation in degree :(kx) 



tan of angle(m2)
(degree) tan
(ak1r ± kxr) 
(akxr)
(akxra) 


slope of 2nd line : (anticlockwise rotation)(m2c) 



slope of 2nd line : (clockwise rotation) (m2d) 



Equn: a2cx +b2cy+c2c =0 
x
+y+=0 


a2dx +b2dy+c2d =0 
x
+y+=0 


coordinate of new point (x2c) & (y2c) 
(x2c)
(y2c) 


coordinate of new point (x2d) & (y2d) 
(x2d)
(y2d) 


yintercept coordinates of line through (x2c,y2c) 
(ix2c)(iy2c) 


yintercept 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 xcoordinate, b
is ycoordinate 
(a) 
(b) 


Local coordinates 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
yinterception point, put the value of (yintx, yinty) or
xinterception 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 anticlockwise or
clockwise direction and you get the new corresponding coordinates
(x2, y2)
x2 =[(y1b)sinθ
+(x1a)cosθ +a]
y2 =[(y1b)cosθ
(x1a)sinθ +b]





