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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 the quadrilateral PQRS.
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 the quadrilateral PQRS.
Class 10 | Exercise 1 | ICSE | Locus | Maths | ML Aggarwal
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 the quadrilateral PQRS.

Following are the steps of Construction:

ML Aggarwal Solutions for Class 10 Chapter 14 Image 40

(i) Construct a line AB = 12 cm.

(ii) Take M as the midpoint of line AB.

(iii) Construct straight lines CD and EF which is parallel to AB at 3 cm distance.

(iv) Taking M as centre and 5 cm radius construct areas which intersect CD at P and Q and EF at R and S.

(v) Now join QR and PS.

now,

PQRS is a rectangle where the length

\[PQ\text{ }=\text{ }8\text{ }cm\]

So the area of rectangle PQRS = PQ × RS

We get

\[\begin{array}{*{35}{l}}

=\text{ }8\text{ }\times \text{ }6  \\

=\text{ }48\text{ }c{{m}^{2}}  \\

\end{array}\]

i

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