Points P, Q, R are said to be collinear if they lie on the same straight line.

The routine returns true if P, Q, and R are collinear; false if they are not; and FAIL if it is unable to determine if the three points are collinear.

If FAIL is returned, and the optional argument cond is given, the condition that makes the points collinear is assigned to this argument.

The command with(geometry,AreCollinear) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{point}\left(A\,0\,0\right),\mathrm{point}\left(B\,2\,0\right),\mathrm{point}\left(C\,-3\,0\right),\mathrm{point}\left(F\,2\,3\right)\:$

$\mathrm{point}\left(M\,\mathrm{mx}\,\mathrm{my}\right)\:$

$\mathrm{AreCollinear}\left(A\,B\,C\right)$

$\mathrm{true}$

$\mathrm{AreCollinear}\left(A\,C\,F\right)$

$\mathrm{false}$

$\mathrm{AreCollinear}\left(A\,F\,M\,'\mathrm{cond}'\right)$

AreCollinear:   "hint: could not determine if 2*my-3*mx is zero"

$\mathrm{FAIL}$

$\mathrm{cond}$

$2\mathrm{my}-3\mathrm{mx}=0$

$\mathrm{assume}\left(\mathrm{cond}\right)$

$\mathrm{AreCollinear}\left(A\,F\,M\right)$

$\mathrm{true}$