Is a point within a triangle?

The problem is a suggested Rosetta Code task- check if a random ( x, y) point lies within a triangle defined by its three corners. The reference gives three different ways of solving this.

Code in Liberty BASIC

    nomainwin

    WindowWidth  =500
    WindowHeight =500

    open "Is a random point inside a triangle?" for graphics_nsb as #wg

    #wg "trapclose quit"

    #wg "down ; fill darkblue ; color cyan ; size 1"

    x1 =200: y1 =400: #wg "set  "; x1; " "; y1
    x2 =400: y2 =400: #wg "goto "; x2; " "; y2
    x3 =300: y3 =100: #wg "goto "; x3; " "; y3
    #wg " goto "; x1; " "; y1
    #wg "flush"

    N =0
    call save N

    do
        x =int( 500 *rnd( 1)): y =int( 500 *rnd( 1))

        a   = ( ( y2 -y3) *( x -x3) +( x3 -x2) *( y -y3)) / ( ( y2 -y3) *(x1 -x3) +( x3 -x2) *( y1 -y3))
        b   = ( ( y3 -y1) *( x -x3) +( x1 -x3) *( y -y3)) / ( ( y2 -y3) *(x1 -x3) +( x3 -x2) *( y1 -y3))
        c   = 1 -a -b

'        p lies in T if and only if 0 <= a <= 1 and 0 <= b <= 1 and 0 <= c <= 1
        if      ( ( 0 <=a) and ( a <=1))_
            and ( ( 0 <=b) and ( b <=1))_
            and ( ( 0 <=c) and ( c <=1))_
        then
            #wg "color green"
        else
            #wg "color red"
        end if
        #wg "set "; x ; " "; y
        scan
        N   =N +1
        if ( N mod 10000) =0 then call save N
    loop until 0

    sub quit h$
        close #h$
        end
    end sub

    sub save N
        #wg "getbmp scr 1 1 500 500"
        'bmpsave "scr", "triangle" +right$( "000000" +str$( N), 6) +".bmp"
        #wg "cls"
        #wg "drawbmp scr 1 1"
    end sub