Edexcel IGCSE Maths
Topic questions Geometry and measures Geometrical problems on coordinate axes
21 questions · 96 marks · about 2 hours
Also involves Coordinate geometry
PQRS is a square.
PR is a diagonal of the square.
P is the point with coordinates (4, 7) R is the point with coordinates (8, –5)
Find an equation of the straight line that passes through the points Q and S Give your answer in the form ay = bx + c where a, b and c are integers.
The diagram shows three points, P, Q and R, marked on a grid.
Write down the coordinates of point P
On the grid, mark with a cross (
) the point with coordinates (3, –1) Label this point T
Find the coordinates of the midpoint of QR
The diagram shows three points, A, B and C, marked on a grid.
Write down the coordinates of A
Find the coordinates of the midpoint of AB
D is the point on the grid so that ABCD is a rectangle.
Find the coordinates of D
The diagram shows three points, A, B and C, marked on a grid.
Write down the coordinates of point A
On the grid, mark with a cross (
) the point D so that ABCD is a rectangle.
Find the coordinates of the midpoint of AC
On the grid, draw the line with equation y = 4
Also involves Coordinate geometry
ABCD is a kite.
AB = AD and CB = CD
The point B has coordinates (k, 1) where k is a negative constant. The point D has coordinates (8, 7)
The straight line L passes through the points B and D
The straight line L is parallel to the line with equation 5y – 3x = 6
Find an equation of AC Give your answer in the form px + qy = r where p, q and r are integers. Show your working clearly.
The diagram shows three points, A, B and C, and a line EF on a grid.
Write down the coordinates of the point A
The coordinates of the point D are (3, –2)
On the grid, mark with a cross (
) the position of D Label the cross D
Find the coordinates of the midpoint of BC
Write down the equation of the line EF
The points A and B are on a coordinate grid.
The coordinates of A are (6, 4) The coordinates of B are (17, j) where j is a constant.
The midpoint of AB has coordinates (k, 15) where k is a constant.
Find the value of j and the value of k
Also involves Linear equations
The points A and B are on a coordinate grid.
The coordinates of A are (6, 4) The coordinates of B are (17, j) where j is a constant.
The midpoint of AB has coordinates (k, 15) where k is a constant.
Find the value of j and the value of k
ABCD is a trapezium with AB parallel to DC
A is the point with coordinates (–4, 6) B is the point with coordinates (2, 3) D is the point with coordinates (–1, 8)
The trapezium has one line of symmetry. The line of symmetry intersects CD at the point E
Work out the coordinates of the point E
The diagram shows three points, A, B and C, on a grid.
Write down the coordinates of
point A
point B
D is the point such that ABCD is a rhombus.
On the grid, mark with a cross (
) the point D Label this point D
Find the coordinates of the midpoint of AB
Also involves Coordinate geometry · Area and perimeter
The straight line L passes through point A (– 6, 2) and point B (5, 3) The straight line M is perpendicular to L and passes through the midpoint of A and B. The line M intersects the line x = – 1 at point C.
Calculate the area of triangle ABC.
Also involves Properties of triangles and quadrilaterals
ABC is an isosceles triangle with AB = AC.
B is the point with coordinates (–1, 5) C is the point with coordinates (2, 10) M is the midpoint of BC.
Find an equation of the line through the points A and M. Give your answer in the form py + qx = r where p, q and r are integers.
Point A has coordinates (–3, 11) Point B has coordinates (47, b) The midpoint of AB has coordinates (a, –19)
Find the value of a and the value of b.
Also involves Linear equations
Point A has coordinates (–3, 11) Point B has coordinates (47, b) The midpoint of AB has coordinates (a, –19)
Find the value of a and the value of b.
Also involves Coordinate geometry
The diagram shows three points, A, B and C, marked on a grid.
Write down the coordinates of point A.
The coordinates of the point D are (–2, –4)
On the grid, mark with a cross (
) the position of D. Label the cross D.
Find the coordinates of the midpoint of BC.
On the grid, draw the line with equation x = 4
The point A has coordinates (5, −4) The point B has coordinates (13, 1)
Work out the coordinates of the midpoint of AB.
Line L has equation y= 2 − 3x
Write down the gradient of line L.
Line L has equation y= 2 − 3x
Does the point with coordinates (100, −302) lie on line L? You must give a reason for your answer.
The point A has coordinates (5, −4) The point B has coordinates (13, 1)
Work out the coordinates of the midpoint of AB.
Line L has equation y= 2 − 3x
Write down the gradient of line L.
Line L has equation y= 2 − 3x
Does the point with coordinates (100, −302) lie on line L? You must give a reason for your answer.
H is the point with coordinates (−4, 1) J is the point with coordinates (j, 15) where j <0 K is the point with coordinates (6, k)
M is the midpoint of JK. The gradient of HM is 2
Find the value of j and the value of k.
P, Q and R are three points marked on a grid.
Write down the coordinates of point Q.
S is the point such that PQRS is a rectangle.
Find the coordinates of point S.
Find the coordinates of the midpoint of PR.
Also involves Straight line graphs
L1 and L2 are two straight lines. The origin of the coordinate axes is O.
L1 has equation 5x + 10y = 8 L2 is perpendicular to L1 and passes through the point with coordinates (8, 6) L2 crosses the x-axis at the point A. L2 intersects the straight line with equation x = –3 at the point B. Find the area of triangle AOB. Show your working clearly.
ABCD is a kite with AB = AD and CB = CD.
B is the point with coordinates (10, 19) D is the point with coordinates (2, 7)
Find an equation of the line AC. Give your answer in the form py + qx = U where p, q and U are integers.
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