A Cartesian Puzzle
The eight sets of coordinates below define various quadrilaterals
(four-sided shapes). In each case one coordinate is missing.
- $(2,11), \; (0,9),\; (2,7),\; (?,?)$
- $(3,7),\; (3,4),\; (8,4),\; (?,?)$
- $(18,3),\; (16,5), \;(12,5),\; (?,?)$
- $(13,12),\; (15,14),\; (12,17),\; (?,?)$
- $(7,14),\; (6,11),\; (7,8),\; (?,?)$
- $(15,9),\; (19,9),\; (16,11),\; (?,?)$
- $(11,3),\; (15,2),\; (16,6),\; (?,?)$
- $(9,16),\; (2,9),\; (9,2),\; (?,?)$
These eight quadrilaterals are all symmetrical. This may be
rotational or line symmetry or both. The shapes are all in the
first quadrant.
The set of eight missing coordinates define another shape - this
time with eight sides which has both rotational and line
symmetry.
Can you draw this new eight-sided shape on a graph like the one
below?
