In the figure below, PQ and QR are drawn to scale.

  1. (a)

    Draw 2 lines, PS and SR so that PQRS is a parallelogram.

  2. (b)

    Measure ∠QPT\angle QPT.

    Answer : (b) ___°

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Worked solution

21(a)

1. Identify the properties of a parallelogram to locate point S

In a parallelogram PQRSPQRS, the opposite sides are parallel and equal in length. Therefore, the vector PS⃗\vec{PS} must be equal to the vector QR⃗\vec{QR}, and SR⃗\vec{SR} must be equal to PQ⃗\vec{PQ}.

2. Locate point S using grid movements

From point QQ to point RR, count the number of grid units horizontally. Since QQ and RR are on the same horizontal line, QR⃗\vec{QR} is purely a horizontal translation to the right. Apply this exact same horizontal translation starting from point PP to locate point SS.

3. Draw the required lines

Draw a straight line segment from PP to SS, and another straight line segment from SS to RR.

Answer

A point S is plotted such that PS is parallel and equal to QR, and SR is parallel and equal to PQ. The lines PS and SR are drawn.

AI analysis — may contain mistakes.

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