Coordinates

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Find the shape and symmetries of the two pieces of this cut cube.

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

What is the area of the triangle formed by these three lines?

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?