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Here are the coordinates of some quadrilaterals, but in each case one coordinate is missing! The coordinates are given going round each quadrilateral in an anti-clockwise direction.
The quadrilaterals are all symmetrical. They may have rotational symmetry, or line symmetry, or both.
Can you work out what the missing coordinates are if you know they are all positive? Is there more than one way to find out?
Now plot those eight missing coordinates on a graph like the one below.
What shape do they make and what sort of symmetry does it have?
This problem is one that requires some familiarity with coordinates in the first quadrant. It will also call on knowledge of both rotational and line symmetry, and properties of various quadrilaterals.
You could play a game of 'twenty questions' to begin with so that pupils get a chance to familiarise themselves with properties of shapes. Choose a quadrilateral and write the name of it on a piece of paper. Invite the class to ask questions to guess what your quadrilateral is, but you can only answer yes or no. Keep a tally of the number of questions asked - if they get it in fewer than twenty, they win, otherwise you win. You could repeat this a few times with pupils choosing shapes.
What kind of quadrilateral do you think this one is?
Where is its fourth vertex?
What kind of symmetry do you think this quadrilateral has? How do you know?
Learners could plot their own quadrilaterals with one vertex of each forming a hexagon and so make a similar problem for a friend to try.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?