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Take any three non – collinear points P, Q, and R. Through each point draw a line parallel to the line joining the other two points.

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Last updated date: 27th Mar 2024
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MVSAT 2024
Answer
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Hint: Join the three points using a pencil and a scale to make a triangle. Through each point of the triangle, use the trick to draw a line parallel to the given line passing through a point. Repeat the process for all the endpoints of the triangle.

Complete step-by-step answer:

We have three collinear points P, Q, and R. We have to draw a line passing through a point, parallel to the line joining the other two points for all the points.
We will join all three points using a pencil and a scale to form a triangle.

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We will now extend all the three line segments PR, QR, and PQ to PA, BR, and PC respectively.
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We will firstly draw a line passing through point R parallel to line PQ.
Taking P as centre and radius smaller than the length of PR, we will draw an arc cutting PR at point E and PQ at point D.
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Taking R as the centre and same radius as the previous arc, we draw another arc cutting the extended line AR at G.
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We will adjust the compass width as DE and with the same radius, taking G as the centre, we cut the arc at point F.
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We will join the point R and F using a pencil and a scale and extend it a bit. Thus, the line RJ passes through R and is parallel to line PQ.
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We will now repeat the procedure as above to draw a line passing through P, parallel to QR, and passing through Q parallel to PQ.
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Hence, we have lines PK, QL, and RJ passing through points P, Q, and R and parallel to the line joining the other two points, as shown in the figure above.

Note: One must keep in mind that all the lines should be straight and must be drawn with a pencil and scale. It’s necessary to label all the vertices during each step of construction. All the constructions must be clear and non – messy and should be drawn using a pencil only.
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