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प्रश्न
Use graph paper for this question. Take 2 cm = 1 unit on both the axes.
- Plot the points A(1, 1), B(5, 3) and C(2, 7).
- Construct the locus of points equidistant from A and B.
- Construct the locus of points equidistant from AB and AC.
- Locate the point P such that PA = PB and P is equidistant from AB and AC.
- Measure and record the length PA in cm.
उत्तर १
Steps of Construction:
- Plot the points A(1, 1), B(5, 3) and C(2, 7) on the graph and join AB, BC and CA
- Now we should join points A and B. Draw perpendicular bisector l of AB. Then, l is the locus of points which are equidistant from A and B.
- Now we should join A and C. Also draw the angle bisector m of ∠CAB. Then, m is the locus of points equidistant from AB and AC.
- Draw the perpendicular bisector of AB and angle bisector of angle A which intersect each other at P. P is the required point. Since P lies on the perpendicular bisector of AB. Therefore, P is equidistant from A and B.
Again,
Since P lies on the angle bisector of angle A.
Therefore, P is equidistant from AB and AC. - On measuring, the length of PA = 2.5 cm
उत्तर २
- Plot the points A(1, 1), B(5, 3) and C(2, 7) as shown.
- Join points A and B. Draw right bisector l of AB. Then, l is the locus of points equidistant from A and B.
- Join A and C. Now draw the bisector m of ∠CAB. Then, m is the locus of points equidistant from AB and AC.
- The point of intersection P of right bisector of AB and angle bisector of ∠CAB is the point such that PA = PB and P is equidistant from AB and AC.
- On measuring PA = 2.5 cm.
संबंधित प्रश्न
Angle ABC = 60° and BA = BC = 8 cm. The mid-points of BA and BC are M and N respectively. Draw and describe the locus of a point which is:
- equidistant from BA and BC.
- 4 cm from M.
- 4 cm from N.
Mark the point P, which is 4 cm from both M and N, and equidistant from BA and BC. Join MP and NP, and describe the figure BMPN.
Construct a triangle ABC, with AB = 6 cm, AC = BC = 9 cm. Find a point 4 cm from A and equidistant from B and C.
Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of lengths 6 cm and 5 cm respectively.
(i) Construct the locus of points, inside the circle, that are equidistant from A and C. prove your construction.
(ii) Construct the locus of points, inside the circle that are equidistant from AB and AC.
Plot the points A(2, 9), B(–1, 3) and C(6, 3) on graph paper. On the same graph paper draw the locus of point A so that the area of ΔABC remains the same as A moves.
Draw and describe the lorus in the following cases:
The lorus of points inside a circle and equidistant from two fixed points on the circle .
Describe completely the locus of point in the following cases:
Centre of a ball, rolling along a straight line on a level floor.
Using ruler and compasses construct:
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of point equidistant from A and C.
(iii) a circle touching AB at A and passing through C.
Without using set squares or protractor construct:
(i) Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
(ii) Draw the locus of a point which moves so that it is always 2.5 cm from B.
(iii) Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
(iv) Mark the point of intersection of the loci with the letter P and measure PC.
Ruler and compass only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct Δ ABC, in which BC = 8 cm, AB = 5 cm, ∠ ABC = 60°.
(ii) Construct the locus of point inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark as P, the point which is equidistant from AB, BC and also equidistant from B and C.
(v) Measure and record the length of PB.
Given ∠BAC (Fig), determine the locus of a point which lies in the interior of ∠BAC and equidistant from two lines AB and AC.
