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Coordinate Geometry (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

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Coordinate Geometry

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1
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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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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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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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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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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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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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A is the point left parenthesis 2 comma space 7 right parenthesis and B is the point left parenthesis – 4 comma space 11 right parenthesis.

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

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

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2
Sme Calculator3 marks

A is the point (7, 2) and B is the point (−5, 8).

Calculate the length of AB.

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3
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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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4
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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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5
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A is the point (2, 1) and B is the point (9, 4).

Find the length of AB.

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6a
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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. 

6b
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Find the co-ordinates of the midpoint of A B.   

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

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7
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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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8a
Sme Calculator3 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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Find the co-ordinates of the mid-point of BC.  

 

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

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9
Sme Calculator3 marks
cie-igcse-2018-march-p4-q10a

Calculate the length of AB.

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1
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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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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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3
Sme Calculator4 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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4
Sme Calculator3 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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