Coordinate Geometry – Exercise 3.1 – (MATHEMATICS) – 9th Class




Exercise 3.1

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

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Sol. Consider the lamp as a point and table as a plane. Choose any two perpendicular edges of the table. Measure the distance of the lamp from the longer edge, suppose it is 25 cm. Again, measure the distance of the lamp from the shorter edge, and suppose it is 30 cm. We can write the position of the lamp as (30, 25) or (25, 30), depending on the order of axes we fix.
Note: Student may suppose different distances from edges.

2. Street Plan: A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city run parallel to these roads and are 200 in apart. There are about 5 streets in each direction. Using 1 cm = 200 in, draw a model of the city on your notebook. Represent the roads I 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 directions. Each cross-street is referred to in the following manner. If the second 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, 7)?

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Sol. The model of Street plan is shown in figure given below.

Let us take East-West as x-axis and North-South as y-axis of coordinates.
Both the cross-streets (4, 3) and (3, 4), are marked in the figure above. They are uniquely found because of the two reference lines we have used for locating them.


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