Geometrical problems on coordinate axes

Here is a sketch of straight line EG.

Work out the coordinates of F.

A straight line passes through points A (– 5, 9), B and C (3, – 7).

AB: BC = 1: 3

Work out the coordinates of point B.

Work out the equation of the line perpendicular to AC that passes through C.

Points P and Q are shown on the grid.

Write down the coordinates of P.

Angle PQR is a right angle. Work out possible coordinates for R.

A (1, 3) and B (2, 9) are points on a centimetre grid.

ABCD is a parallelogram. AD and BC are horizontal and each has length 5 cm The diagonals of ABCD cross at E. Work out the two possible pairs of coordinates of E.

P is the point (2, 14) Q is the point (6, 8) R is the point (2, 5) Use gradients to show that angle PQR is not a right angle.

Line AB is shown where A is the point (1, 0) and B is the point (5, 8)

P is a point on AB. The distance AP is half the distance AB. Work out the coordinates of P.

A line is drawn from B that is parallel to the x-axis meets the y-axis at point Q. Work out the coordinates of Q.

A is (2, 13) and B is (10, 1) Circle the midpoint of AB.

(4, 6) (5, 6.5) (6, 7) (8, 12)

A line joins A (1, 1) and B (6, 1) on a centimetre grid.

P is a point on the line AB such that AP: PB = 2: 3 C is a point such that angle APC is 90 ° and PC = 4 cm Write down the coordinates of the two possible points for C.

P is (4, 9) and Q is (–2, 1) Circle the midpoint of PQ.

(1, 5) (3, 4) (3, 5) (6, 8)

A (0, 2) and B (6, 5) are points on the straight line ABCD.

AB = BC = CD Work out the coordinates of D.

A (0, 2) and B (6, 5) are points on the straight line ABCD.

AB = BC = CD Work out the coordinates of D.

A is (2, 12) and B is (8, 2) Circle the midpoint of AB. (3, 5) (4, 6) (5, 7) (6, 10)