MATHS 3 Marks Question

Draw a line l and take a point P outside l.
With centre P, draw an arc so that it cuts the line l at two points, say A and B.
We shall find the perpendicular bisector of the line segment AB.
With centres at A and B, draw arcs of equal radius above and below AB.
Let the arcs intersect at the points C and D.
Join CD and extend it, if P is not on this line.
The line CD is perpendicular to the given line l and passes through the given point P.

Draw a vertical line AB.
With the centre at A, draw an arc.
With centre at C, draw an arc intersecting the arc at D and E.
Join AD and AE and extend these lines.

Take points F on AD and G on AE such that AF = AG.
Let M and N be the midpoints of AF and AG, respectively.
Using a compass, draw semicircles on the lines MF, AM, AN, and NG.
Erase the extra letters, lines, and arcs to get the required arch design.

Let ABCD be a square. We draw perpendicular bisectors of the sides AB and BC as shown in the figure.

Let the perpendicular bisectors intersect the square at the points P, Q, R, and S.
With centres at P, Q, R, and S, draw semicircles in the square with radius equal to AP.
Colour the boundary of the design using a coloured pencil.
This will make the design stand out from the supporting lines and curve.