Using a ruler and a pair of compasses construct
Ai.) quadrilateral PQRS such that /PQ/=7cm,<QPS=60°,/PS/=6.5cm,<PQR=135°,and /QS/=QR
ii.) Locus L¹ of point equidistant from P and Q
iii.) Locus L² of point equidistant from P and S
Bi.) Label the point T where L¹ and L² interset
ii.) With center T and radius /TP/ construct a cirlce L³
see the related questions below for very similar constructions.
To construct the quadrilateral PQRS, follow these steps:
1. Start by drawing a straight line segment PQ of 7 cm.
2. With P as the center, use the compass to draw an arc with a radius of 6.5 cm. This arc should intersect the line segment PQ at point S.
3. With Q as the center, use the compass to draw an arc with a radius of 6.5 cm. This arc should intersect the line segment PQ at point R.
4. Finally, connect points R and S to complete the quadrilateral PQRS.
To construct the locus L¹ of points equidistant from P and Q, follow these steps:
1. Draw a line segment PQ of any length.
2. Place the compass on point P and extend it to point Q.
3. Draw arcs from both P and Q with the same radius to intersect, forming two points of intersection. Label these points A and B.
4. Repeat steps 2 and 3 from a different point on line PQ, and find two more points of intersection C and D.
5. Continue repeating steps 2 and 3 from various points on line PQ.
6. The locus L¹ is the set of all points that lie on the line passing through the points of intersection (A, B, C, D, and so on).
To construct the locus L² of points equidistant from P and S, follow these steps:
1. Draw a line perpendicular to PS at point S. This line represents the perpendicular bisector of PS.
2. With S as the center, use the compass to draw an arc with a radius greater than half of PS. This arc should intersect the perpendicular bisector at two points, labeled M and N.
3. Repeat steps 1 and 2 at different points on line PS.
4. The locus L² is the set of all points that lie on the perpendicular bisector of PS.
To label the point T where loci L¹ and L² intersect, follow these steps:
1. Find any point of intersection between loci L¹ and L², and label it T.
To construct a circle L³ with center T and radius TP, follow these steps:
1. With T as the center, use the compass to draw a circle with a radius equal to the length of TP.
2. This circle represents L³, the locus of points equidistant from point T.