Pythagoras' theorem

AC is a straight line. A is the point (– 3, 2) B is the midpoint of the line AC. B is the point (12, 10)

Work out the coordinates of C.

Work out the distance AB.

All lengths shown are in centimetres.

Use Pythagoras’ theorem to show that 4w² – 8w – 21 = 0

Work out the size of angle x.

ABCDEF is a triangular prism. ABCD is a rectangle and angle BCF is 90 ° AB = 14 cm BC = 8 cm CF = 6 cm M is the midpoint of EF.

Work out the size of angle BMD.

Points A (– 12, 1) and B (12, – 1) lie on a circle. AB is a diameter of the circle.

Work out the equation of the circle.

ABCDEFGH is a cuboid.

Work out the length AG.

S (7, 2) and T (5, – 4) are points on a straight line.

Work out the gradient of the line.

Work out the distance between S and T. Give your answer in the form a where a and b are both integers greater than 1

VABCD is a pyramid. The square horizontal base, ABCD, has side length 15 cm V is directly above the centre, X, of the base. VA = 28 cm

Work out the size of the angle that VA makes with ABCD.

Work out the length of BC.

A (– 2, 5) and B (4, 13) are points on a circle. AB is a diameter.

Work out the equation of the circle. Give your answer in the form (x – a)² + (y – b)² = c where a, b and c are integers.

ABCDEFGH is a cuboid.

AB = 40 cm BC = 9 cm CG = 20 cm P is a point on HG such that HP: PG = 3: 7 AP = 25 cm

Work out the size of angle APC.

Work out the distance between the points A (– 3, 7) and B (5, 1)

ABCDEFGH is a cube with side length 32 cm M and N are points on DH and CG respectively.

Work out the size of the angle that the line BM makes with the plane ABCD.