### There are 17 results

Broad Topics >

Coordinates and Coordinate Geometry > Coordinates

##### Age 16 to 18 Challenge Level:

What on earth are polar coordinates, and why would you want to use them?

##### Age 16 to 18 Challenge Level:

Three equilateral triangles ABC, AYX and XZB are drawn with the
point X a moveable point on AB. The points P, Q and R are the
centres of the three triangles. What can you say about triangle
PQR?

##### Age 14 to 18 Challenge Level:

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?

##### Age 16 to 18 Challenge Level:

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?

##### Age 14 to 16 Challenge Level:

A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

This is a beautiful result involving a parabola and parallels.

##### Age 16 to 18 Challenge Level:

Investigate the number of points with integer coordinates on
circles with centres at the origin for which the square of the
radius is a power of 5.

##### Age 14 to 16 Challenge Level:

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

##### Age 14 to 18 Challenge Level:

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

##### Age 14 to 16 Challenge Level:

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

##### Age 14 to 16 Challenge Level:

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

##### Age 14 to 16 Challenge Level:

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?

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16

Scientist Bryan Rickett has a vision of the future - and it is one
in which self-parking cars prowl the tarmac plains, hunting down
suitable parking spots and manoeuvring elegantly into them.

##### Age 14 to 16 Challenge Level:

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?