Q1. How will you describe the position of a table lamp on your study table to another person?
Answer 1. Give two independent, perpendicular references so the position is fixed exactly.
Examples you can use (any one clear pair is fine):
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“The lamp is 12 cm from the left edge of the table and 8 cm from the back edge.”
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Or using a simple grid on the tabletop: “It sits at column 3, row 2 (counting from the left and from the back).”
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Or relative to corners: “2 cm right and 5 cm forward from the top-left corner of the table.”
(Any description that gives a distance along a horizontal direction and a distance along a perpendicular vertical direction uniquely locates the lamp.)
Q2. (Street Plan)
A city has two main roads which cross 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 m apart. There are 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).
Answer 2.
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Step to draw (brief): On graph paper, draw 5 equally spaced vertical lines (N–S streets) and 5 equally spaced horizontal lines (E–W streets). With the chosen scale 1 cm = 200 m, spacing between successive lines will be 1 cm. Label the vertical streets 1 to 5 (say from left to right) and horizontal streets 1 to 5 (say from bottom to top). Each intersection corresponds to an ordered pair (i, j) where i = N–S street number, j = E–W street number.
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(i) Exactly one cross-street is referred to as (4, 3).
Reason: (4,3) means the intersection of the 4th N–S street and the 3rd E–W street — that pairing determines a unique crossing. -
(ii) Exactly one cross-street is referred to as (3, 4).
Reason: (3,4) is the distinct intersection of the 3rd N–S street with the 4th E–W street. (Note: (4,3) and (3,4) are different intersections unless the 3rd and 4th labels coincide, which they do not.)
Extra note: With 5 streets in each direction there are distinct intersections in the model.