TEXTBOOK REFERENCE · GANITA MANJARI
End-of-Chapter Q14 · Open official source ↗
A city has two main roads which cross each other at the centre of the city. These two roads are along the North–South (N–S) direction and East–West (E–W) direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 10 streets in each direction.
(i) Using 1 cm = 200 m, draw a model of the city in your notebook. Represent the roads/streets by single lines.
(ii) There are street intersections in the model. Each street intersection is formed by two streets — one running in the N–S direction and another in the E–W direction. Each street intersection is referred to in the following manner: If the second street running in the N–S direction and street in the E–W direction meet at some crossing, then we call this street intersection . Using this convention, find:
(a) how many street intersections can be referred to as .
(b) how many street intersections can be referred to as .
AIMS worked solution
AIMS SOLUTION / EXPLANATION
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Given:
Two perpendicular main roads and parallel streets at uniform spacing.
To Find:
A model and the number of crossings named and .
Property:
Two nonparallel straight lines have one intersection.
Solution:
Draw the main roads at right angles through the model centre. Draw the stated streets parallel to them, with adjacent streets 1 cm apart.
Label the streets consistently with the textbook convention; the first entry selects a north–south street and the second an east–west street.
selects one pair of streets, hence one crossing. selects another pair, also one crossing.
Results:
One intersection for each label; the two locations differ.
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