Mathematics
Use ruler and compasses only for the following question. All construction lines and arcs must be clearly shown.
(i) Construct a △ABC in which BC = 6.5 cm, ∠ABC = 60° and AB = 5 cm.
(ii) Construct the locus of points at a distance of 3.5 cm from A.
(iii) Construct the locus of points equidistant from AC and BC.
(iv) 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.
Answer
(i) Steps of construction :
Draw a line segment BC = 6.5 cm.
With B as center draw an arc BX, at an angle of 60°.
From BX cut off BA = 5 cm.
Join AC. Hence, ABC is the required triangle.
With A as center draw a circle of radius = 3.5 cm.
Draw CZ, the angle bisector of ∠C.
Mark the points as X and Y where CZ intersects circle with center A.
(ii) The locus of points at a distance of 3.5 cm from A is a circle with radius = 3.5 cm and center A.
(iii) The locus of points equidistant from AC and BC is CZ, the angle bisector of ∠C.
(iv) On measuring, XY = 4.8 cm.
Related Questions
On a graph paper, draw the line x = 6. Now on the same graph paper, draw the locus of the point which moves in such a way that its distance from the given line is always equal to 3 units.
Ruler and compasses 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 the assessment.
(i) Construct a triangle ABC, in which BC = 6 cm, AB = 9 cm, and ∠ABC = 60°.
(ii) Construct the locus of all points, inside △ABC, which are equidistant from B and C.
(iii) Construct the locus of the vertices of the triangles with BC as base, which are equal in area to △ABC.
(iv) Mark the point Q, in your construction, which would make △QBC equal in area to △ABC, and isosceles.
(v) Measure and record the length of CQ.
Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.
Construct a triangle BCP given BC = 5 cm, BP = 4 cm and ∠PBC = 45°.
(i) Complete the rectangle ABCD such that :
(a) P is equidistant from AB and BC.
(b) P is equidistant from C and D.
(ii) Measure and record the length of AB.