(a) Using ruler a pair of compasses only…

Question 1 Report

(a) Using ruler a pair of compasses only, construct:

(i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\(^o\), QR||PS, |PS| =10.6 cm, and IPRI = 93 cm;

(ii) locus \(l_1\) of points equidistant from P and R;

(iii) locus \(l_2\) of points equidistant from Q and R

(b) Measure: (i) |QR|;

ii. < PSR

iii. |QY|, where Y is the point of intersection h and h.

Answer

Answer Details

(a) Construction (ruler and compasses only).

Draw \(|PQ| = 6.8\) cm. At Q construct \(\angle PQR = 120^{\circ}\) and draw the ray along which R lies.
Through P draw a line parallel to QR (since \(QR \parallel PS\)) and mark \(|PS| = 10.6\) cm. The diagonal \(|PR| = 9.3\) cm (arc from P) fixes R on its ray. Join R to S to complete trapezium PQRS.
\(l_1\): construct the perpendicular bisector of \(PR\) (points equidistant from P and R).
\(l_2\): construct the perpendicular bisector of \(QR\) (points equidistant from Q and R). Let \(l_1\) and \(l_2\) meet at Y.

(b) Expected measurements from an accurate drawing:

(Accept small tolerances, since these are read off the construction.)

(a) Using ruler a pair of compasses only, construct: (i) a trapezium PQRS such that |PQ| = 6.8 cm, < PQR = 120\(^o\), QR||PS, |PS| =10.6 cm, and IPRI = 93 c...