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प्रश्न
In Δ ABC, B and Care fixed points. Find the locus of point A which moves such that the area of Δ ABC remains the same.
उत्तर
Steps of Construction:
(i) ABC is the required triangle.
(ii) Draw perpendicular bisector of BC which intersects BA in M, then any point on LM is equidistant from Band C.
(iii) Through A, draw a line m 11 BC.
(iv) The perpendicular bisector of BC and the parallel line m intersect each other at Q.
(v) Then triangle QBC is equal in area to triangle ABC. mis the locus of all points through which any triangle with base BC will be equal in area of triangle ABC.
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संबंधित प्रश्न
Describe the locus of vertices of all isosceles triangles having a common base.
State the locus of a point in a rhombus ABCD, which is equidistant
- from AB and AD;
- from the vertices A and C.
Construct a rhombus ABCD with sides of length 5 cm and diagonal AC of length 6 cm. Measure ∠ ABC. Find the point R on AD such that RB = RC. Measure the length of AR.
Construct a ti.PQR, in which PQ=S. 5 cm, QR=3. 2 cm and PR=4.8 cm. Draw the locus of a point which moves so that it is always 2.5 cm from Q.
In given figure, ABCD is a kite. AB = AD and BC =CD. Prove that the diagona AC is the perpendirular bisector of the diagonal BD.
In Δ PQR, bisectors of ∠ PQR and ∠ PRQ meet at I. Prove that I is equidistant from the three sides of the triangle , and PI bisects ∠ QPR .
Draw and describe the lorus in the following cases:
The lorus of a point in rhombus ABCD which is equidistant from AB and AD .
Draw and describe the locus in the following cases :
The locus of a point in the rhombus ABCD which is equidistant from the point A and C
Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.
- Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
- Construct the locus of points at a distance of 3.5 cm from A.
- Construct the locus of points equidistant from AC and BC.
- Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.
Use ruler and compasses only for the following questions:
Construct triangle BCP, when CB = 5 cm, BP = 4 cm, ∠PBC = 45°.
Complete the rectangle ABCD such that :
(i) P is equidistant from AB and BC and
(ii) P is equidistant from C and D. Measure and write down the length of AB.
