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Coordinate Geometry : Exercise 3.1 (Mathematics NCERT Class 9th)


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Q.1     How will you describe the position of a table lamp on your study table to another person?
Sol.

Consider the lamp as a point P and table as a plane. Choose any two perpendicular edges of the table , say OX and OY. Measure the distance of the lamp i.e., P from the longer edge OX, let it be 30 cm. Again, measure the distance of the lamp P from the shorter edge OY,  let it be 20 cm.

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 Thus, the position of the lamp P referred to the edges OX and OY is (20, 30).


 

Q.2      (Street Plan) : A city has two main roads which cross each other at the center of the city. These two roads are along the North - south direction and East West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross- street is  made  by two streets, one running in the North- South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North- South direction and 5th in the East- West direction meet at some crossing, then we will call this cross- street (2, 5). Using this convention, find :
(i) How many cross- streets can be referred to as (4, 3)
(ii) How many cross- streets can be referred to as (3, 4)
Sol.

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Street plan is as shown in the figure :
(i) There is only one cross street, which can be referred as (4, 3).
(ii) There is only one cross street, which can be referred as (3, 4).



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