Line On Northing And Easting Coordinate Plane

Line on Northing and Easting Coordinate Plane DE12 = (E2-E1) P2:(N2,E2)

N2 Az Azimuth of the Line N1

DN12 = (N2-N1)

P1 E1*m

NE=0 m = slope = DN12/DE12

Tan(Az)= DE12 DN12

E1 0 E1

E2

For any Point P on the Line defined by 2 points (P1,P2) with coordinates (N,E) Say P:(N, E) N = ( N2-N1) * E + NE=0 ( E2-E1 )

NE=0 = The N-Axis intercept (i.e. N when E is 0)

N = DN12*E + NE=0 = m*E + NE=0 DE12 We can see that NE=0 = N1-E1*m = N1-E1*(DN12/DE12) = N1-E1*(( N2-N1)/(E2-E1)) NE=0 = N1-E1*1/Tan(Az) = N1-E1*Cot(Az) N = ( N2-N1) * E + N1-E1*( N2-N1) ( E2-E1 ) ( E2-E1 )

= ( N2-N1) *(E-E1) + N1 = DN12*(E-E1)+N1 ( E2-E1 ) DE12

N=(1/Tan(Az))*E+N1-E1*(1/Tan(Az))=Cot(Az)*E+N1-E1*Cot(Az)=Cot(Az)*( E-E1)+N1

If P1:(N1,E1) = P1:(500.000,300.000) and P2 = P2:(800.000.900.000) DP12:(DN12,DE12) = DP12:(800.000-500.000,900.000-300.000) = DP12:(300.000,600.000) N = (300.000/600.000)*E+500.000-(300.000)*(300.000/600.000) N = ( 0.500000)*E + 500.000-(300.000)*(0.500000) N = (0.500000)*E + 350.000

Line on Northing and Easting Coordinate Plane DE12 = (E2-E1) P2:(N2,E2)

N2 Az Azimuth of the Line N1

DN12 = (N2-N1)

P1 E1*m

NE=0 m = slope = DN12/DE12 m=Cot(Az)

E1

Tan(Az)= DE12 DN12

0 E1

E2

N = m*E + N1 – m*E1 = m*(E-E1) + N1 N = Cot(Az)*E + N1 – Cot(Az)*E1 = Cot(Az)*(E-E1) + N1 N=(1/Tan(Az))*E+N1-E1*(1/Tan(Az))=Cot(Az)*E+N1-E1*Cot(Az)=Cot(Az)*( E-E1)+N1

If P1:(N1,E1) = P1:(500.000,300.000) And Az12 = 63± 26’ 05.8” N= Cot(Az12)*E+N1-E1*Cot(Az12) N= Cot(63± 26’ 05.8”)*E+N1-E1*Cot(63± 26’ 05.8”) N= (0.500000)*E + 500.000 – 150.000 N= (0.500000)*E + 350.000