Mathematics
Draw a line segment AB of length 12 cm. Mark M, the mid-point of AB. Draw and describe the locus of a point which is
(i) at a distance of 3 cm from AB.
(ii) at a distance of 5 cm from the point M.
Mark the points P, Q, R, S which satisfy both the above conditions. What kind of quadrilateral is PQRS ? Compute the area of quadrilateral PQRS.
Locus
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Answer
The figure is shown below:
(i) Draw the line segment CD and EF parallel to AB, at a distance of 3 cm from it.
Hence, the locus is a pair of straight lines at a distance of 3 cm from AB.
(ii) Mark M as the mid-point of AB. Take M as center and radius 5 cm draw a circle.
Hence, the locus is a circle with center M and radius 5 cm.
(iii) The circle meets the segments CD and EF at P, Q, R and S.
P, Q, R and S are joined to form a rectangle.
Area of rectangle = Length × Breadth = PQ × PR.
On measuring PQ = 8cm.
So, Area = 8 × 6 = 48 cm2.
Hence, PQRS is a square and area is 48 cm2.
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