CAIE IGCSE Mathematics Extended E3.4 Length & midpoint Question Bank

Practise finding lengths and midpoints of line segments from coordinates, including exact surd lengths and geometry decisions.

Syllabus
2028–2030
Topic
E3.4
Level
Extended

Exam points

  • calculate line lengths from coordinate differences using Pythagoras, including surd form
  • find midpoint coordinates by averaging the x-values and y-values separately
  • compare calculated side lengths to decide whether a triangle is scalene, isosceles or equilateral

Covered syllabus points

E3.4.1 Calculate the length of a line segment.E3.4.2 Find the coordinates of the midpoint of a line segment.

E3.4 Length and midpoint question 1

[Maximum number: 5]

Question (a)

(a)

P has coordinates (-1,3) and Q has coordinates (6,4).

[ 5 ]

Question (i)

(i)

Find the coordinates of the midpoint of PQ.

[ 2 ]

Question (ii)

(ii)

Find the length PQ.

[ 3 ]

E3.4 Length and midpoint question 2

[Maximum number: 2]

A is the point (3,7) and B is the point (-1,5).

Find the coordinates of the midpoint of the line AB.
(

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