Calculation example - Find the coordinates of the intersection of two lines

Calculate the coordinates of the intersection of two lines given the coordinates of four stations.

Known values:

Coordinates A (E_A, N_A), B (E_B, N_B), C (E_C, N_C), D (E_D, N_D)

i.e.

A             E 250      N 530

B             E 510      N 1130

C             E 1390   N 1180

D             E 1760   N 150

Solution: Coordinates of intersection point X (E_X, N_X)

The equation of line AC:

i.e.

thus

Similarly, the equation of line BD:

i.e.

thus

Subtracting (1) from (2),

Substituting in equation (1),