Draw two parallel lines at a distance of 4.5 cm apart

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Then, we mark a point on the plane of paper which is at a distance of $4.5$ centimeters from the line drawn already. We label the point as $P$.

Now, we know that parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always equidistant from each other. Also, parallel lines have equal directional ratios. Now, we draw the required line and name it as line $m$.

Therefore, we get the construction required as above.

Note: We should have a strong grip over the concepts of basic coordinate and analytical geometry and construction in order to deal with such questions. One must be open to mathematical ideas and construction methods to innovate and analyze the steps of construction required to get to the final result. We should know the fact that parallel lines are always equidistant to each other in order to solve the problem. One can also mark more points at a distance of $4.5$ centimeter in order to be sure of the final construction.

Question 4 Constructions Exercise 17.1

Answer:

Steps of construction:

Draw a line PQ.
Take any two points A and B on the line.
Construct ∠PBF = 90o and ∠QAE = 90o
With A as center and radius 5 cm cut AE at C.
With B as center and radius 5 cm cut BF at D.
Join CD and produce it on either side to get the required line parallel to AB and at a distance of 5 cm from it.

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Draw two parallel lines at a distance of 4.5 cm apart

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