MathPickle (Gordon Hamilton in Calgary, Canada) have a task 'quadrilaterals on a grid' where students are asked to find special quadrilaterals on a 5 by 5 dotty grid with
(a) the biggest area and (b) the smallest area
with a restriction that the top left dot of the grid must be one of the quadrilateral's vertices
the task links to 'complete the quadrilateral'
MathPickle go on to consider a 9 by 9 dotty grid, with two fixed vertices, at (5, 2) and (1, 5)
this is presented on the MathPickle youtube (from 3.00 on) clip