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Draw and describe the locus in each of the following cases: (i) The locus of points at a distance 2.5 cm from a fixed line. (ii) The locus of vertices of all isosceles triangles having a common base.
Draw and describe the locus in each of the following cases: (i) The locus of points at a distance 2.5 cm from a fixed line. (ii) The locus of vertices of all isosceles triangles having a common base.
Class 10 | Exercise 1 | ICSE | Locus | Maths | ML Aggarwal
Draw and describe the locus in each of the following cases: (i) The locus of points at a distance 2.5 cm from a fixed line. (ii) The locus of vertices of all isosceles triangles having a common base.

(i) 1. Construct a line AB.

2. Construct lines l and m  parallel to AB at a distance of 2.5 cm.

now,

lines l and m are the locus of point P at a distance of 2.5 cm.

ML Aggarwal Solutions for Class 10 Chapter 14 Image 7

(ii) According to ques,

Δ ABC is an isosceles triangle where AB = AC.

Taking A as centre construct a perpendicular AD to BC.

Here AD is the locus of point A which are the vertices of Δ ABC

In Δ ABD and Δ ACD

The sides AD = AD is common

according to ques,

Hypotenuse AB = AC

According to RHS Axiom

Δ ABD = Δ ACD

BD = DC (c.p.c.t)

hence, locus of vertices of isosceles triangles having common base is the perpendicular bisector of BC.

i

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