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Just Opposite

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?

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Pentagon

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

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Beelines

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

Ladder and Cube

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
A cube (1 metre by 1 metre by 1 metre) has one face on the ground and one face pushed up against a wall.

A 4 metre long ladder is leaning against the wall, just touching the cube.




How high is the top of the ladder above the ground?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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