हिंदी

On a graph paper, draw the lines x = 3 and y = –5. Now, on the same graph paper, draw the locus of the point which is equidistant from the given lines.

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प्रश्न

On a graph paper, draw the lines x = 3 and y = –5. Now, on the same graph paper, draw the locus of the point which is equidistant from the given lines.

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उत्तर

 
On the graph, draw axis XOX’ and YOY’

Draw a line l, x = 3 which is parallel to y-axis 

And draw another line m, y = –5, which is parallel to x-axis

These two lines intersect each other at P.

Now draw the angle bisector p of angle P.

Since p is the angle bisector of P, any point on P is equidistant from l and m.

Therefore, this line p is equidistant from l and m.

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अध्याय 16: Loci (Locus and Its Constructions) - Exercise 16 (A) [पृष्ठ २३८]

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सेलिना Concise Mathematics [English] Class 10 ICSE
अध्याय 16 Loci (Locus and Its Constructions)
Exercise 16 (A) | Q 19. | पृष्ठ २३८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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 graph paper for this question. Take 2 cm = 1 unit on both the axes.

  1. Plot the points A(1, 1), B(5, 3) and C(2, 7).
  2. Construct the locus of points equidistant from A and B.
  3. Construct the locus of points equidistant from AB and AC.
  4. Locate the point P such that PA = PB and P is equidistant from AB and AC.
  5. Measure and record the length PA in cm. 

Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these Iines and also 2 cm away from their point of intersection. How many such points exist? 


Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD. 


Draw and describe the locus in the following case:

The locus of a point in rhombus ABCD which is equidistant from AB and AD.


Describe completely the locus of a point in the following case:

Centre of a circle of varying radius and touching the two arms of ∠ ABC. 


Describe completely the locus of a point in the following case:

Centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O. 


Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.

  1. Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
  2. Construct the locus of points at a distance of 3.5 cm from A.
  3. Construct the locus of points equidistant from AC and BC.
  4. 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.

State and draw the locus of a point equidistant from two given parallel lines.


Without using set squares or protractor.
(i) Construct a ΔABC, given BC = 4 cm, angle B = 75° and CA = 6 cm.
(ii) Find the point P such that PB = PC and P is equidistant from the side BC and BA. Measure AP.


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