NCERT Solutions for Class 7th Maths Chapter 6 A Pointed Arch — In-text Questions
Book page 150 Updated on2026-09-19
Q1.
How do we construct this shape?The pointed arch shape of Fig. 6.11, page 150.What supporting lines will you use to draw this arch?
Answer
The supporting lines are just two line segments of equal length meeting at the top — the same idea as 'Wavy Wave' from Grade 6.
Draw the base and mark the two springing points, P and Q.
Draw two segments PT and QT of equal length meeting at a point T above the base. They form the skeleton of the pointed arch.
Mark the midpoint of each segment with the perpendicular-bisector construction.
Draw an arc from P to T, and a matching arc from Q to T, using centres chosen on the perpendicular bisectors of PT and QT.
The two arcs meet at T in a point — that is the pointed top.
Why it happens: equal supporting segments make the two halves mirror images. Because both arcs end at the same top point T and start at the same height, the arch closes cleanly at the apex instead of rounding off. Curving the arcs one way gives an ogee (S-shaped) profile; curving them the other way gives the plain pointed arch of the photograph.
Q2.
If their midpoints are marked, will you be able to construct a pointed arch?
Answer
Yes. The midpoint is exactly what the arc needs.
Let M be the midpoint of the supporting segment PT.
Every centre that gives an arc through both P and T
must be equidistant from P and T
⇒ it lies on the perpendicular bisector of PT, which passes through M.
Choose any point on that perpendicular bisector as the centre;
set the compass to its distance from P; sweep from P to T.
Why it happens: this is the very first property of the chapter again — a point is equally far from P and T exactly when it lies on the perpendicular bisector of PT. Marking the midpoint gives you a point of that bisector, so you can draw the bisector and pick your centre anywhere along it. Moving the centre further out flattens the arc; bringing it closer to M makes the arc bulge.
Tip: use the same distance-from-the-midpoint on both sides, otherwise the left half of the arch will bulge more than the right half.