CAIE IGCSE Mathematics Shortest Distance Problems

Practise recognising the perpendicular from a point to a line as the shortest distance and calculating it with triangle methods.

Exam points

draw or identify the perpendicular from the point to the target line as the required shortest distance
calculate the perpendicular length with a suitable sine, cosine, tangent or equal-area relationship
derive any preceding side or angle before using the right triangle containing the distance

[Maximum number: 3]

NOT TO SCALE

The diagram shows a field, ABCD with B north of A.
BD is a path across the field.
$A B=85 \mathrm{~m}, A D=72 \mathrm{~m}, B D=129 \mathrm{~m}$ , angle $B D C=39^{\circ}$ and angle $B C D=60^{\circ}$ .

Find the shortest distance from A to BD.

44.5 or 44.51 to 44.54
M2 for implicit correct method, e.g. $\frac{d}{85}=\sin31.6^\circ$ oe
or M1 for recognition that the line from A is perpendicular to BD

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E6.2.3 Know that the perpendicular distance from a point to a line is the question 1