Syllabus Edition

First teaching 2021

Last exams 2024

|

Coordinate Geometry (CIE IGCSE Maths: Extended)

Exam Questions

1 hour21 questions
1
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2 marks

A is the point left parenthesis 2 comma space 3 right parenthesis and B is the point left parenthesis 7 comma negative 5 right parenthesis.

Find the co-ordinates of the midpoint of AB.
 

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

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2
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1 mark

cie-igcse-2018-oct-nov-p4-tz1-q8a 
Write down the co-ordinates of A.
 

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

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3
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2 marks

A line joins A left parenthesis 1 comma space 3 right parenthesis to B left parenthesis 5 comma space 8 right parenthesis.

Find the midpoint of A B.

 

left parenthesis........................ , ........................right parenthesis 

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4
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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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5a
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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.
5b
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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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6
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2 marks

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

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1
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3 marks

The coordinates of P are left parenthesis negative 3 comma space 8 right parenthesis and the coordinates of Q are left parenthesis 9 comma negative 2 right parenthesis.

Calculate the length PQ.

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2
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3 marks

A rhombus A B C D has a diagonal A C where A is the point left parenthesis negative 3 comma space 10 right parenthesis and C is the point left parenthesis 4 comma space minus 4 right parenthesis.

Calculate the length A C.

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3
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3 marks

A is the point (2, 1) and B is the point (9, 4).

Find the length of AB.

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4a
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3 marks

A is the point left parenthesis 8 comma 5 right parenthesis and B is the point left parenthesis negative 4 comma 1 right parenthesis.

Calculate the length of A B. 

4b
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2 marks

Find the co-ordinates of the midpoint of A B. 
 

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

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5
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3 marks

A is the point left parenthesis 7 comma 12 right parenthesisand B is the point left parenthesis 2 comma negative 1 right parenthesis.

Find the length of A B.

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6
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2 marks

Find the mid-point of A B where A equals left parenthesis w space comma space r right parenthesis and  B equals left parenthesis 3 w space comma space t right parenthesis.
Give your answer in its simplest form in terms of w, r and t.
 

left parenthesis..................... , .....................right parenthesis

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7
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3 marks

cie-igcse-2018-march-p4-q10a

Calculate the length of AB.

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8a
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3 marks

cie-igcse-2018-oct-nov-p4-tz1-q8a

C is the point (8, 14).

Calculate the length of AC.

8b
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2 marks

Find the co-ordinates of the mid-point of BC.
 

 

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

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1
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7 marks

The graphs of space y equals open parentheses x minus 1 close parentheses squared space and space y equals fraction numerator 1 space over denominator 2 end fraction x plus 1 space intersect at A and B.
 
Find the length of AB.
 

AB = ................................................

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2
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3 marks

A straight line joins the points left parenthesis 3 k comma space 6 right parenthesis and left parenthesis k comma space minus 5 right parenthesis.
The line has a gradient of 2.

Find the value of k.

k = ................................................... 

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3
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2 marks

P is the point (16, 9) and Q is the point (22, 24).

N is the point on PQ such that PN = 2NQ.
Find the co-ordinates of N.

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

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4a
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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.

4b
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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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5
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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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6
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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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7
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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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