Coordinates

There are 53 NRICH Mathematical resources connected to Coordinates
Just Opposite
problem

Just opposite

Age
14 to 16
Challenge level
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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?
Rational Round
problem

Rational round

Age
16 to 18
Challenge level
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Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
Two Number Lines
problem

Two number lines

Age
7 to 11
Challenge level
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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?
A Shade Crossed
problem

A shade crossed

Age
14 to 16
Challenge level
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Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
Graphical Triangle
problem

Graphical triangle

Age
14 to 16
Challenge level
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What is the area of the triangle formed by these three lines?
Cushion Ball
problem

Cushion ball

Age
16 to 18
Challenge level
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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?
Napoleon's Hat
problem

Napoleon's hat

Age
16 to 18
Challenge level
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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?

Mesh
problem

Mesh

Age
16 to 18
Challenge level
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A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?
Plane to See
problem

Plane to see

Age
16 to 18
Challenge level
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P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
Something in Common
problem

Something in common

Age
14 to 16
Challenge level
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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.