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Broad Topics > Coordinates and Coordinate Geometry > Coordinates

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A Cartesian Puzzle

Stage: 2 Challenge Level: Challenge Level:1

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

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Coordinate Tan

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

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Parabella

Stage: 5 Challenge Level: Challenge Level:1

This is a beautiful result involving a parabola and parallels.

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Beelines

Stage: 4 Challenge Level: Challenge Level:1

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

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Ladder and Cube

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Polar Bearings

Stage: 5 Challenge Level: Challenge Level:1

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

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Coordinate Patterns

Stage: 3 and 4 Challenge Level: Challenge Level:1

This task requires learners to explain and help others, asking and answering questions.

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Parallel Parking

Stage: 4

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.

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An Introduction to Polar Coordinates

Stage: 4 and 5

This introduction to polar coordinates describes what is an effective way to specify position. This article explains how to convert between polar and cartesian coordinates and also encourages the. . . .

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Cartesian Isometric

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

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Lost on Alpha Prime

Stage: 4 Challenge Level: Challenge Level:1

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

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Something in Common

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Coordinating Classroom Coordinates

Stage: 2

This article describes a practical approach to enhance the teaching and learning of coordinates.

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Going Places with Mathematicians

Stage: 2 and 3

This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping. . . .

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A Shade Crossed

Stage: 4 Challenge Level: Challenge Level:1

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

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Rational Round

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Corridors

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Complex Rotations

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Choose some complex numbers and mark them by points on a graph. Multiply your numbers by i once, twice, three times, four times, ..., n times? What happens?

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Snookered

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Coordinate Cunning

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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Criss Cross Quiz

Stage: 2 Challenge Level: Challenge Level:1

A game for 2 players. Practises subtraction or other maths operations knowledge.

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A Tilted Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Square Pair Circles

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Grid Points on Hyperbolas

Stage: 5 Challenge Level: Challenge Level:1

Find a condition which determines whether the hyperbola y^2 - x^2 = k contains any points with integer coordinates.

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Napoleon's Hat

Stage: 5 Challenge Level: Challenge Level:1

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?

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Cushion Ball

Stage: 5 Challenge Level: Challenge Level:1

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?

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Pentagon

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the vertices of a pentagon given the midpoints of its sides.

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Just Opposite

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?