Geometrical problems on coordinate axes

In the diagram A is the point (0, 8) B is the point (16, 0) The point D divides the line segment AB in the ratio 1: 3 The line L passes thr h D.

L passes through the point with coordinates (–2,f) Show that f –4

Write down the coordinates of point A.

On the grid, mark with a cross () the point D so that ABCD is a square. Label this point D.

On the grid, mark with a cross () the point E so that C is the midpoint of BE. Label this point E.

ABC is a straight line.

Point A has coordinates (2, 7) Point B has coordinates (8, 12)

Find the coordinates of point C.

ABC is a straight line.

Point A has coordinates (2, 7) Point B has coordinates (8, 12)

Find the coordinates of point C.

A is the point with coordinates (7, 13) B is the point with coordinates (−3, 21) C is the point with coordinates (15, 23) M is the midpoint of AB. N is the midpoint of BC. Work out the distance between M and N. Give your answer correct to 1 decimal place.

The points L, M and N are such that LMN is a straight line. The coordinates of L are (−3, 1) The coordinates of M are (4, 9) Given that LM: MN = 2: 3, find the coordinates of N.

The points L, M and N are such that LMN is a straight line. The coordinates of L are (−3, 1) The coordinates of M are (4, 9) Given that LM: MN = 2: 3, find the coordinates of N.

Here is a sketch of the line L.

The points P(–6, 0) and Q(0, 3) are points on the line L. The point R is such that PQR is a straight line and PQ:QR = 2: 3

Find the coordinates of R.

Find an equation of the line that is perpendicular to L and passes through Q.

A pattern is made from four identical rectangles. The sides of the rectangles are parallel to the axes.

Point A has coordinates (3, 4) Point B has coordinates (11, 20) Point C is marked on the diagram. Work out the coordinates of C. You must show all your working.