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The Lily Pond

Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go?

A Cartesian Puzzle

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Transformation Tease

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?

Dotty Relationship

Age 7 to 11
Challenge Level

Thank you to those of you who sent in solutions.

Several of you including Shuaib correctly identified that the lines AB and CD cross at $90$ degrees. Flora observes that the number of squares horizontally and vertically are swapped around when you draw a perpendicular line:

They are the same number of squares although the number of squares has been rotated.

Flora goes on to observe that there is more than one solution each time :

because perpendicular lines can be any distance apart.

Alden and Jimmy from Woodstock Primary correctly point out that :

They do not have to be the same length because they can be any length as long as it's a $90$ degree angle.