formula for line 1:   Y = (D - A) * X + A
formula for line 2:   Y = (C - B) * X + B

intersection: X and Y coordinates of line1 and line2 are equal ...

(D - A) * X + A = (C - B) * X + B

reduces to =>  X = (B - A) / (D - A - C + B)

plug X into equation for line 1 gives ...

Y = (D - A) * (B - A) / (D - A - C + B) + A