Question 17
Use support lines in Fig. 6.11 to construct a pointed arch. Make different arches, by changing the radius of the arcs.
We will draw two arcs from two points to create a pointed arch.
Step 1 — Mark the centers
Look at the bottom part of Fig. 6.11. It shows two lines meeting at a point. Let us call this meeting point V. There are two dots on these lines. Let us call the dot on the left line A. Let us call the dot on the right line B. Points A and B will be the centers for our arcs.
Step 2 — Choose a radius
We need to decide how big our arch will be. This is done by choosing a length for our compass. Let us call this length the radius, or r. You can choose any length for r. Make sure it is long enough for the arcs to meet.
Step 3 — Draw the first arc
Place the sharp point of your compass on point A. Open the compass so its pencil tip is at your chosen radius r. Draw a curved line upwards from point A. This is our first arc.
Step 4 — Draw the second arc
Now, place the sharp point of your compass on point B. Make sure your compass is still open to the same radius r. Draw another curved line upwards from point B. This is our second arc.
Step 5 — Find the arch's peak
The two arcs you drew will cross each other. Let us call this crossing point C. This point C is the very top, or peak, of our pointed arch. The two arcs, from A to C and from B to C, together form the pointed arch.
Step 6 — Make different arches
To make a different pointed arch, simply repeat steps 2 to 5. This time, choose a different radius r. If you choose a smaller radius, the arch will look taller and narrower. If you choose a larger radius, the arch will look wider and flatter. You can make many different arches by just changing the radius.
Answer
(i) Identify the two marked points on the slanted lines as the centers for the arcs. (ii) Choose a specific radius for the compass. (iii) Draw an arc from each center using this chosen radius. (iv) Ensure the two arcs intersect above the vertex of the lines. (v) The intersecting arcs form the pointed arch. (vi) To make different arches, change the radius of the arcs and repeat the steps.
More questions in FIO
When constructing the perpendicular bisector, is it necessary to have the same radius for the arcs above and below XY? Explore this through construction, and then justify your answer.
[Hint 1: Any point that is of the same distance from X and Y lies on the perpendicular bisector.
Hint 2: We can draw the whole line if any two of its points are known.]
Is it necessary to construct the pairs of arcs above and below XY? Instead, can we construct both the pairs of arcs on the same side of XY? Explore this through construction, and then justify your answer.
While constructing one pair of intersecting arcs, is it necessary that we use the same radii for both of them ? Explore this through construction, and then justify your answer.
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Construct the following figure.
Use support lines in Fig. 6.11 to construct a pointed arch. Make different arches, by changing the radius of the arcs.
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[Hint: Find the angles in this figure.]
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[Hint: Find a line segment on whose perpendicular bisector passes through P.]
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