Coordinate Geometry (Edexcel GCSE Maths)

Exam Questions

2 hours37 questions
1
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2 marks

The point A has coordinates (2, 3).
The point B has coordinates (6, 8).

M is the midpoint of the line A B.
Find the coordinates of M.

q1-easy-2-15-cordinate-geometry-edexcel-gcse-maths

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2
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2 marks

The straight line bold L has equation 2 y plus 7 x equals 10

Find the gradient of bold L.

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3
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2 marks

Point A has coordinates (5, 8)
Point B has coordinates (9, –4)

Work out the gradient of A B.

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4a
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2 marks

The point A has coordinates (5, −4)
The point B has coordinates (13, 1)

Work out the coordinates of the midpoint of A B.

4b
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1 mark

Line bold L has equation y space equals space 2 space minus space 3 x

Write down the gradient of line bold L.

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5
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2 marks

Find the gradient of the straight line with equation  5 x plus 2 y equals 7.

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6
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1 mark

A is (2, 13) and B is (10, 1)

Circle the midpoint of A B.

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

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7
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1 mark

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

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

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8
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1 mark

Circle the point that does not lie on the curve   y space equals space x cubed

open parentheses negative 1 half comma space minus 1 over 8 close parentheses left parenthesis 5 comma space 125 right parenthesis open parentheses 1 third comma space 1 over 9 close parentheses left parenthesis – 1 comma space – 1 right parenthesis

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9
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1 mark

A is (2, 12) and B is (8, 2)

Circle the midpoint of A B.

left parenthesis 3 comma space 5 right parenthesis (4, 6) (5, 7) (6, 10)

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10
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2 marks

Work out the gradient of the straight line through (–2, 3) and (1, 9)

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11
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2 marks

The diagram shows an octagon

q9-paper-1h-nov-2021-aqa-gcse-maths

x space equals space 1 spaceand y space equals space 5 are lines of symmetry.

Work out the coordinates of point Q.

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12a
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1 mark

A straight line is drawn on the centimetre grid.

q12-paper-2h-june-2018-aqa-gcse-maths

Fay assumes that the scale is 1 cm represents 1 unit.

Use her assumption to work out the gradient of the line.

12b
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1 mark

In fact, the scale is 1 cm represents 2 units.

Which statement is correct?
Tick one box.

square      The answer to part (a) is too big

size 26px square        The answer to part (a) stays the same

size 26px square        The answer to part (a) is too small

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1a
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2 marks

kJ1G4dGj_q1-medium-2-15-cordinate-geometry-edexcel-gcse-maths

A is the point (—1, 2)
B is the point (7, 5)

Find the coordinates of the midpoint of A B.

1b
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2 marks

P is the point (—4, 4)
Q is the point (1, —5)

Find the gradient of P Q.

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2
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2 marks

q2-medium-2-15-cordinate-geometry-edexcel-gcse-maths

Point P has coordinates (5, 7).
Point M has coordinates (1, 2.5).

Point M is the midpoint of the line P Q.

Find the coordinates of point Q.

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3
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1 mark

Here are the equations of four straight lines.

Line A   y space equals space 2 x space plus space 4
Line B  2 y space equals space x space plus space 4
Line C  2 x space plus space 2 space y space equals space 4
Line D  2 x space long dash y space equals space 4

Two of these lines are parallel.

Write down the two parallel lines?

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4
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2 marks

Point A has coordinates left parenthesis – 3 comma space 11 right parenthesis
Point B has coordinates left parenthesis 47 comma space b right parenthesis
The midpoint of A B has coordinates left parenthesis a comma space – 19 right parenthesis

Find the value of a and the value of b.

a = ................................................     
b = ................................................     

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5
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3 marks

P is the point (2, 14)
Q is the point (6, 8)
R spaceis the point (2, 5)

Use gradients to show that angle P Q R is not a right angle.

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6
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3 marks

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

q7-paper-1h-june-2018-aqa-gcse-maths

A B space equals space B C space equals space C D
Work out the coordinates of D.

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7a
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2 marks

A is the point (2, –5)

B is the point (4, –9)

Show that the gradient of the straight line passing through A and B is –2

7b
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2 marks

C is the point (–301, 601)

Does space C spacelie on the straight line passing through space A spaceand B?

You must show your working.

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8
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2 marks

A comma space B and C are points on the axes as shown.

q21-paper1h-nov2017-aqa-gcse-maths

The area of triangle A B C is 28 square units.

Work out possible coordinates for A comma space B and C.

A ( ......... , .......... )

B ( ......... , .......... )

C ( ......... , .......... )

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1
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2 marks

Here is a cuboid drawn on a 3-D grid.

q1-hard-2-15-cordinate-geometry-edexcel-gcse-maths

P is a vertex of the cuboid.

T divides the line O P in the ratio 1 : 2

Find the coordinates of T.

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2a
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2 marks

A and space B spaceare two points.

Point A has coordinates (—2, 4).
Point B has coordinates (8, 9).

C is the midpoint of the line segment A B.

Find the coordinates of C.

2b
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3 marks

D is the point with coordinates (100, 56).

Does point D lie on the straight line that passes through A and B?
You must show how you work out your answer.

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3
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3 marks

The points space A comma space B space and C lie in order on a straight line.

The coordinates of A are (2, 5)
The coordinates of B are (4, p)
The coordinates of C are (q, 17)

Given that A C space equals space 4 A B, find the values of p and q.

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4
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3 marks

Q comma space R and S are points on a grid.

Q is the point with coordinates (106, 103)
R is the point with coordinates (106, 105)
S is the point with coordinates (104, 105.5)

P and A are two other points on the grid such that

   R is the midpoint of P Q
   S is the midpoint of P A

Work out the coordinates of the point A.

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5
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4 marks

A triangle has vertices P comma space Q and R.

The coordinates of P are (—3, —6)
The coordinates of Q are (1, 4)
The coordinates of R are (5, —2)

M is the midpoint of P Q.
N is the midpoint of Q R.

Prove that M N is parallel to P R.
You must show each stage of your working.

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6
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5 marks

A pattern is made from four identical squares.

The sides of the squares are parallel to the axes.

q6-hard-2-15-cordinate-geometry-edexcel-gcse-maths

Point A has coordinates (6, 7)
Point B has coordinates (38, 36)
Point C is marked on the diagram.

Work out the coordinates of C.

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7
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2 marks

A B is a line segment.

A is the point with coordinates (3, 6, 7).
The midpoint of A B has coordinates (—2, 2, 5).

Find the coordinates of B.

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8
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3 marks

bold A and bold B are straight lines.
Line bold A has equation 2 y space equals space 3 x space plus space 8
Line bold B goes through the points left parenthesis long dash 1 comma space 2 right parenthesis and left parenthesis 2 comma space 8 right parenthesis

Do lines bold A and bold B intersect?
You must show all your working.

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9a
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4 marks

A rectangle space A B C D is to be drawn on a centimetre grid such that

A has coordinates (–4, –2)
B has coordinates (1, 10)
C has coordinates (19, a)
D has coordinates left parenthesis b comma space c right parenthesis

Work out the value of a, the value of b and the value of c.

a equals................................. space space
b equals................................. space
c equals................................. space

9b
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3 marks

Calculate the perimeter, in centimetres, of rectangle ABCD.

...................................................... cm

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10
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4 marks

The diagram shows a line joining O to P.

q28-paper3h-specimen2015-aqa-gcse-maths

The gradient of the line is 2

The length of the line is square root of 2645

Work out the coordinates of P.

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11
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5 marks

A pattern is made from four congruent right-angled triangles.

q7-paper5-nov2020-ocr-gcse-maths

The line AC is parallel to the x - axis.
The point A has coordinates (4, 9) and the point B has coordinates (17, 12).

Work out the coordinates of point C and point D.

C space left parenthesis space........................... space comma space.......................... right parenthesis space
D space left parenthesis space........................... space comma space.......................... right parenthesis

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12
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3 marks

A straight line goes through the points (p comma space q) and (r comma space s), where

  • p space plus space 2 space equals space r
  • q space plus space 4 space equals space s.

Find the gradient of the line.

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1
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5 marks

A B C is a triangle in which angle A B C space equals space 90 degree

p and q are integers such that


the coordinates of space A are left parenthesis space p comma space 10 space right parenthesis
the coordinates of B are (–1, –5 )
the coordinates of space C spaceare left parenthesis 8 comma space q right parenthesis

Given that the gradient of A C is negative 6 over 7
work out the value of p and the value of q

p = .......................................................      
q = .......................................................      

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2
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6 marks

The straight line bold L has equation     x space – space y space equals space 3
The curve bold C has equation 3 x squared – space y squared plus space x y space equals space 9

bold L and bold C intersect at the points P and Q.

Find the coordinates of the midpoint of P Q.
Show clear algebraic working.

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3
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6 marks

Triangle H J K is isosceles with H J space equals space H K and J K space equals space square root of 80

H is the point with coordinates left parenthesis negative 4 comma space 1 right parenthesis
J is the point with coordinates left parenthesis j comma space 15 right parenthesis where j space less than space 0
K is the point with coordinates left parenthesis 6 comma space k right parenthesis

M spaceis the midpoint of J K.
The gradient of H M is 2

Find the value of space j spaceand the value of k.

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4
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6 marks

The curve with equation x squared – space x space plus space y squared space equals space 10 and the straight line with equation x space – space y space equals space – 4 intersect at the points Aand B.

Work out the exact length of A B.
Show your working clearly and give your answer in the form fraction numerator square root of a over denominator 2 end fraction where a is an integer.

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5
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6 marks

The curve with equation y space equals space left parenthesis 10 x space minus space 3 right parenthesis left parenthesis x space plus space 1 right parenthesis and the line with equation y space minus space 6 x space equals space 0 intersect at the points A and B.

Find the coordinates of the midpoint of A B.
Show your working clearly.

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