CAIE IGCSE Mathematics Extended E3.4.2 Find the Coordinates of the Midpoint of a Line Segment Questions

Practise Extended CAIE IGCSE Mathematics by averaging endpoint coordinates and interpreting segment midpoints.

Exam points

Calculate the midpoint of a line segment from the coordinates of its endpoints.
Apply the midpoint formula separately to the x- and y-coordinates.
Interpret the midpoint as equidistant from the two endpoints.

[Maximum number: 5]

Figure for Question CAIE IGCSE Mathematics Extended E3.4.2 Find the Coordinates of the Midpoint of a Line Segment Questions question 1 — CAIE IGCSE Mathematics Extended

The diagram shows a shape made from a major sector AOB and triangles OBC and AOD. $O B=6 \mathrm{~cm}, B C=2 \mathrm{~cm}$ , obtuse angle $A O C=135^{\circ}$ and angle $B C O=90^{\circ}$ .

C is the midpoint of OD.
Calculate AD.

16.1 or 16.10 to 16.13
M2 for $2\times\sqrt{6^2-2^2}$ oe or $2\times6\cos19.5$ oe
or M1 for $OC^2+2^2=6^2$ oe or $6\cos19.5$ or better
AND M2 for $\sqrt{6^2+\text{their }OD^2-2\times6\times\text{their }OD\times\cos135}$
or M1 for expression under the square root
A1 for 259 to 260

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CAIE IGCSE Mathematics Extended E3.4.2 Find the Coordinates of the Midpoint of a Line Segment Questions question 1