座標幾何 coordiante geometry

For the sake of convenience , let D=(u,v)
the equation of AC :
(y-b)/(x-a)=(b-q)/(a-p)
y=(b-q)(x-a)/(a-p)+b---(1)
the equation of BD :
(y-n)/(x-m)=(v-n)/(u-m)
y=(v-n)(x-m)/(u-m)+n---(2)
Sub (2) into (1) ,
(b-q)(x-a)/(a-p)+b=(v-n)(x-m)/(u-m)+n
[(b-q)/(a-p)-(v-n)(u-m)]x=[m(v-n)/(u-m)+a(b-q)/(a-p)]+n-b
x={[m(v-n)/(u-m)+a(b-q)/(a-p)]+n-b}/[(b-q)/(a-p)-(v-n)(u-m)]
y=(v-n)({{[m(v-n)/(u-m)+a(b-q)/(a-p)]+n-b}/[(b-q)/(a-p)-(v-n)(u-m)]}-m)/(u-m)+n
Hence , the intersection point =({[m(v-n)/(u-m)+a(b-q)/(a-p)]+n-b}/[(b-q)/(a-p)-(v-n)(u-m)]) ,(v-n)({{[m(v-n)/(u-m)+a(b-q)/(a-p)]+n-b}/[(b-q)/(a-p)-(v-n)(u-m)]}-m)/(u-m)+n)