CAIE IGCSE Mathematics Extended E6.2.3 Know That the Perpendicular Distance From a Point to a Line Is the Questions

Practise recognising that the perpendicular is the shortest distance from a point to a line, then calculate it using trigonometry or area relationships.

Exam points

Draw or identify the perpendicular from a point to a line as the required shortest distance.
Calculate the perpendicular distance using a suitable sine, cosine, tangent or equal-area relationship.
Derive a required side or angle before using the right triangle containing the shortest distance.

[Maximum number: 3]

Figure for Question CAIE IGCSE Mathematics Extended E6.2.3 Know That the Perpendicular Distance From a Point to a Line Is the Questions question 1 — CAIE IGCSE Mathematics Extended

\section*{NOT TO SCALE}

The diagram shows a quadrilateral ABCD.
$C D=10 \mathrm{~m}$ and $D B=12 \mathrm{~m}$ .
Angle $D B A=90^{\circ}$ , angle $C D B=56^{\circ}$ and angle $A D B=34^{\circ}$ .

Calculate the shortest distance from B to the line AD.

6.71 or 6.706 to $6.710 \ldots$

M2 for $\sin 34=\frac{\text { dist }}{12}$ oe or
$\frac{1}{2} \times 12 \times$ their $(a)=\frac{1}{2} \times$ theirAD × dist oe
or M1 for recognition of perpendicular distance

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CAIE IGCSE Mathematics Extended E6.2.3 Know That the Perpendicular Distance From a Point to a Line Is the Questions question 1