Mathematics
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.
Answer
Steps of construction :
Draw a line l, x = 6 which is parallel to y-axis.
At a distance of 3 units on both sides from x = 6 mark points P and Q.
Draw line m and n parallel to l and through P and Q respectively.
From figure,
Equation of m : x = 3 and Equation of n : x = 9.
Hence, locus of the point which moves in such a way that its distance from the given line is always equal to 3 units are lines x = 3 and x = 9.
Related Questions
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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.